minerals

Article Quantitative Phase Analysis of Skarn Rocks by the Rietveld Method Using X-ray Powder Diffraction Data

Yana Tzvetanova 1 , Ognyan Petrov 1, Thomas Kerestedjian 2,* and Mihail Tarassov 1

1 Institute of Mineralogy and Crystallography, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria; [email protected] (Y.T.); [email protected] (O.P.); [email protected] (M.T.) 2 Geological Institute, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., 24 Bl., 1113 Sofia, Bulgaria * Correspondence: [email protected]



Received: 9 September 2020; Accepted: 7 October 2020; Published: 9 October 2020


Abstract: The Rietveld method using X-ray powder diffraction data was applied to selected skarn samples for quantitative determination of the present minerals. The specimens include garnet, clinopyroxene–garnet, plagioclase–clinopyroxene–wollastonite–garnet, plagioclase–clinopyroxene– wollastonite, plagioclase–clinopyroxene–wollastonite–epidote, and plagioclase– clinopyroxene skarns. The rocks are coarse- to fine-grained and characterized by an uneven distribution of the constituent minerals. The traditional methods for quantitative analysis (point-counting and norm calculations) are not applicable for such inhomogeneous samples containing minerals with highly variable chemical compositions. Up to eight individual mineral phases have been measured in each sample. To obtain the mineral quantities in the skarn rocks preliminary optical microscopy and chemical investigation by electron probe microanalysis (EPMA) were performed for the identification of some starting components for the Rietveld analysis and to make comparison with the Rietveld X-ray powder diffraction results. All of the refinements are acceptable, as can be judged by the standard indices of agreement and by the visual fits of the observed and calculated diffraction profiles. A good correlation between the refined mineral compositions and the data of the EPMA measurements was achieved.

Keywords: quantitative phase analysis; skarn minerals; Rietveld method

1. Introduction The estimation of relative quantities of the constituent minerals in rocks is essential for their classification and determination of paragenesis as well as for studies of their genesis, sequence of different mineralogical stages and geological events. The mineral modal analysis is also important for assessment of potentially valuable minerals and is applied in multi-component systems such as cements, ceramics, and archaeological materials. The Rietveld method is one of the most appropriate techniques for modal analysis of rocks and synthetic polycrystalline materials based on X-ray powder diffraction (XRPD). This method was originally developed for the refinement of structures studied with neutron-diffraction [1,2] and subsequently was successfully applied to crystal-structure refinements of minerals and synthetic equivalents investigated with X-ray powder diffraction and synchrotron radiation [3–6]. This methodology and the possibilities for quantitative analysis were developed in detail in the works of: Albinati and Willis [7], Hill [8], Hill and Madsen [9], Hill and Howard [10], Bish and Howard [11], Post and Bish [12], Snyder and Bish [13], Hill [14], Young [15]. The Rietveld XRPD method is a full-profile approach for quantitative analysis based on a least squares fit between the calculated diffraction pattern and the observed experimental data of a measured

Minerals 2020, 10, 894; doi:10.3390/min10100894 www.mdpi.com/journal/minerals Minerals 2020, 10, 894 2 of 30 diffraction pattern. In this technique, the simulated XRPD pattern is calculated from the structural parameters of each mineral (atomic coordinates, site occupancies, unit cell parameters, etc.), the scale factor for each constituent phase, experimental parameters affecting the pattern, effects resulting from preferred orientation, crystallite size and degree of microstrain, parameters describing the peak profile and the background. The phase abundances are directly calculated from the refined scale-factors. The quantitative mineralogical analysis using Rietveld XRPD method has significant advantages over other traditional methods such as (i) point-counting or image analyses of thin sections, (ii) conventional X-ray powder-diffraction measurements using integrated peak-intensities, and (iii) normative calculations based on whole-rock chemical composition [16]. One of the main advantages is that during the analytical procedure the crystal chemistry and physical properties of each of the phases can be adjusted. The possibility to refine the unit cell parameters, occupancy and site coordinates allows extracting additional information from the powder diffraction pattern [17]. A detailed review of the advantages and disadvantages of each of the above methods was made by Hill et al. [18]. Systematic results on the application of Rietveld XRPD quantitative analysis to geological samples have been reported by Hill et al. [18] for determination of mineral abundances in a range of igneous, volcanic, and metamorphic rocks, by Mumme et al. [19] in sedimentary rocks, and by Mumme et al. [20] in massive sulfide ores. The method was successfully applied to various geological materials—montmorillonite rocks [21]; wollastonite skarns [22]; hydrothermally altered rocks [23]; heavy minerals in sandstones [24]; dacitic rocks [25]; pyrite and other sulfide minerals in mine rock piles [26]; bentonites [27]; zeolites and amorphous phases in zeolitized tuffaceous rocks [28]; granitic pegmatite [29]; ultramafic rocks [30]; mineral concentrations in bauxite residues [31]; carbonate rocks containing Mg-rich calcite and non-stoichiometric dolomite [32]; hydroxy-interlayered smectite in soils [33]. The Rietveld XRPD method is now considered as the most flexible and accurate one for determination of mineral abundances, especially when examining inhomogeneous rocks containing areas with significant differences in grain size or fine-zoned rocks such as various types of skarns. In general, most skarn minerals (such as garnet, pyroxene, melilite, epidote, olivine, amphibole, plagioclase, etc.) show marked compositional variations not only within one zone but also within an individual crystal due to local heterogeneous skarn formation conditions. In this case, the determination of mineral contents by routine methods (point-counting in thin sections or whole-rock analyses) is not suited. Additionally, X-ray diffraction patterns of skarns are complex, with hundreds of overlapping peaks, which make it difficult to find any peaks suitable for measuring integrated intensities. The aim of the present paper is to demonstrate the abilities of the Rietveld XRPD method for quantitative determination of minerals in skarn samples from Zvezdel–Pcheloyad Pb-Zn ore deposit (Eastern Rhodopes, Bulgaria), containing chemically variable crystalline phases. This methodology is fast, inexpensive and accurate. Optical study and electron probe microanalysis were performed in order to make comparisons with the Rietveld XRPD results. The obtained data provide important mineralogical information with possibilities for genetic interpretations. The results can be used in petrological studies when quantitative analysis of similar inhomogeneous samples with analogous mineral composition is required.

2. Geological Setting Skarn xenoliths were found to occur in mine gallery No 68 from the Zvezdel–Pcheloyad Pb-Zn ore deposit hosted by monzonitic rocks of the second intrusive phase of the Zvezdel pluton [34]. The Zvezdel pluton is the biggest monzonitic intrusion in the Bulgarian part of the East Rhodopes and is intruded into the comagmatic Paleogene basaltic andesites to trachybasaltic andesites of the Zvezdel volcano. The skarns are zoned, forming bands less than 20 cm in width. The contacts between the different zones are often unclear due to mineralization caused by late stage fluids. The cores of the skarn xenoliths consist of coarse-grained garnet and clinopyroxene–garnet domains in a quartz–calcitic matrix, surrounded Minerals 2020, 10, 894 3 of 30 by wollastonite-bearing zones. Based on mineral paragenesis the following zones are determined from the proximal parts of the xenoliths towards the contact with the monzonitic rock: garnet (Grt), clinopyroxene–garnet (Cpx-Grt), plagioclase–clinopyroxene–wollastonite–garnet (Pl-Cpx-Wo-Grt), plagioclase–clinopyroxene–wollastonite (Pl-Cpx-Wo), plagioclase–clinopyroxene–wollastonite–epidote (Pl-Cpx-Wo-Ep), and plagioclase–clinopyroxene (Pl-Cpx). Quartz and calcite are characteristic for all zones. Titanite, apatite, magnetite, and Ti-rich garnets are present as accessory minerals [35]. According to mineral assemblages two main stages of the skarn-forming processes have been distinguished—magmatic (high temperature contact metamorphic) and postmagmatic one [35]. The magmatic stage is represented by melilite (gehlenite 62.5–33.5%, åkermanite 40.6–22.9%, Na-melilite 16.3–4.0%, Fe-åkermanite 10.9–0.1%, Na-Fe3+-melilite 10.3–0.0%), “fassaitic” clinopyroxene with a high 3+ content of the Ca-Tschermak and esseneite components (11.39–17.75 wt% Al2O3, Fe —0.180–0.487 apfu), and wollastonite 2M (I generation). The minerals of this stage are observed as relicts in garnets − of the postmagmatic stage. The presence of “fassaitic” clinopyroxene and melilite suggests high temperature conditions (above 800 ◦C) in a shallow depth (Phd) before crystallization of the monzonitic magma—estimated by a two-feldspar geothermometer at about 675 ◦C[34]. The products of this stage are subsequently overprinted by anhydrous metasomatic assemblages of the postmagmatic stage: Ti-rich garnets (TiO2 content of 8.04–13.10 wt%, schorlomite component—18.95–31.77%), garnets of the grossular–andradite series (Adr96.61–3.10), “fassaitic” clinopyroxene (II generation), clinopyroxene of the diopside–hedenbergite series (Di ), wollastonite 2M (II generation), and plagioclase 91.17–27.12 − (Ab100–3.30). The wollastonite was determined as 2M polytype using single-crystal XRD structure refinement [36]. Early epidote is also assigned to this stage. The mineral assemblage associated with final phase of hydrothermal activity (retrograde processes) is dominated by late epidote, prehnite, chlorite, fracture-filling thaumasite, gypsum, and zeolite [35].

3. Materials and Methods

3.1. Materials All rock samples used in the present study were collected from the skarn xenoliths from the Zvezdel–Pcheloyad ore deposit. After preliminary X-ray phase analysis, optical and electron microprobe studies of six well-characterized samples were chosen to represent the different skarn zones for quantitative analysis.

3.2. Optical and SEM/EPMA Methods Polished thin sections were prepared from each sample for examination under optical polarizing microscope. The minerals in the samples were determined by standard optical methods using a Leitz Orthoplan microscope (Ernst Leitz GmbH, Wetzlar, Germany). The chemical compositions of selected individual phases in each thin section were determined by ZEISS EVO 25LS (Carl Zeiss SMT Ltd, Cambridge, England) scanning electron microscope equipped with an EDAX Trident (AMETEK, EDAX Inc., Mahwah, NJ, USA) system at 16 kV accelerating voltage, about 1 nA beam current, using reference standards. Optical and electron probe microanalysis (EPMA) were used for precise mineral identification and to compare with the XRPD-derived mineral compositions. Representative EPMA analyses and structural formulae of studied skarn minerals are given in the AppendixA (Tables A1–A7).

3.3. XRPD Data Collection and Rietveld Refinement The selected samples for quantitative analysis were ground to optimum grain-size for XRPD analysis (<10 µm) and pressed from the bottom of the sample holder in order to minimize partially preferred orientation of anisotropic grains. Step-scan X-ray powder diffraction data was collected over a range of 4–80 2θ with CuKα radiation on D2 Phaser—Bruker AXS Bragg–Brentano diffractometer operated at 30 kV and 10 mA with a step size of 0.02 2θ and a counting time of 4 s/step. The identification Minerals 2020, 10, 894 4 of 30 of all minerals was performed using powder diffraction files of the International Centre for Diffraction Data—ICDD, PDF2 database [37]. The phase quantification procedure involved the identification of the mineral phases followed by subsequent quantitative phase analysis of all data sets using the full profile Rietveld method implemented in the FullProf Suite Program, version July 2017 [38–40]. For the samples with more complex mineralogy containing phases with marked anisotropy, we used the Topas v4.2 software [41]. The crystal structure parameters used as starting models of each of the component phases were taken from literature sources (Table1).

Table 1. Sources of crystal structure data used to derive starting models of the minerals for the quantitative phase analysis.

Mineral Sources of Crystal Structure Data Albite Armbruster et al. (1990) [42] Labradorite Wenk et al. (1980) [43] Andradite Lager et al. (1989) [44] Grossular Hasen and Finger (1978) [45] Diopside Levien and Prewitt (1981) [46] Hedenbergite Cameron et al. (1973) [47] Esseneite Cosca and Peacor (1987) [48] Wollastonite 2M Hesse (1984) [49] Epidote Dollase (1971) [50] Prehnite Papike and Zoltai (1967) [51] Calcite Effenberger et al. (1981) [52] Quartz Levien et al. (1980) [53] Chlorite Zanazzi et al. (2009) [54]

The sequence of parameters, which were refined, is the following: scale factors for all phases, zero-shift parameter, background polynomial coefficients, unit-cell parameters for each phase, half-width parameters, atomic site occupancies, atomic coordinates, and preferred orientation. Details of the Rietveld refinement strategy and suggested guidelines are reported by Hill and Madsen [9,55] and Young et al. [56]. A correction for preferred orientation (exponential function implemented in the program Fullprof and preferred orientation spherical harmonics in Topas v4.2 software) was refined for minerals with marked grain-shape anisotropy (feldspars, pyroxene, wollastonite, calcite, epidote, chlorite, etc.). The effect of preferred orientation on the scale factors of the phases is minimized by Rietveld full profile fitting, especially for phases with a large number of XRPD reflexes [13]. The unit cell parameters and the atomic site occupancies of the major minerals with expressed isomorphism were set as variables in the final cycles of refinement (e.g., the Ca and Na content of the feldspars, the Mg and Fe content of the pyroxenes, Al and Fe content of the garnets). The chemical composition determined by EPMA was assigned to the minor minerals present. The fit of the calculated profile with the measured XRPD pattern gives scale factors for each phase which are related to the weight fractions by Equation (1) [10]: X Wp = Sp(ZMV)p/ i Si(ZMV)i (1) where S, Z, M and V are, respectively, the Rietveld scale factor, the number of formula units per unit cell, the mass of the formula unit and the unit-cell volume. The quality of the fit between the calculated and observed diffraction profiles obtained in a Rietveld refinement is usually given with the standard agreement indices Rp, Rwp, Rexp and the goodness of fit index (GofF), defined by Young et al. [15]. Minerals 2020, 10, 894 5 of 30

4. Results

4.1. Garnet Skarn

MineralsThe 2020 garnet, 10, x FOR zone PEER is dominantly REVIEW composed of garnets, calcite and quartz with minor prehnite5 of and 27 chlorite. Magnetite, apatite and titanite occur as accessory minerals. The grain-size of the rock varies in a a very very wide wide range—from range—from a a few few microns microns to to 4 4mm. mm. Coarse-grained Coarse-grained euhedral euhedral garnet garnet crystals crystals occur occur in ain fine-grained a fine-grained quartz–calcite–grossular quartz–calcite–grossular matrix matrix (Figure (Figure 1a,b).1a,b). Due Due to to the the presence ofof fine-grainedfine-grained material, an optical mode was not applicable for this sample. Based on optical characteristics and electron pr probeobe microanalyses, different different garnet generations were identified.identified. The The earliest garnets are are Ti-rich (TiO 2 fromfrom 5.30 wt% to 11.23 wt% and schorlomite component up to 31.8%) and under under plane plane polarized polarized li lightght they they appear appear as as brow brownn to to red-brown red-brown isotropic isotropic crystals (Figure 11c,d).c,d). TheThe secondsecond generationgeneration isis representedrepresented byby coarse-grainedcoarse-grained garnets,garnets, whichwhich belongbelong to the grossular–andraditegrossular–andradite solidsolid solutionsolution rangingranging inin compositioncomposition fromfrom AdrAdr8.58.5GrsGrs88.688.6 toto almost pure andradite Adr94.3GrsGrs2.82.8 withwith spessartine, spessartine, pyrope, pyrope, almandine, almandine, uvarovite, uvarovite, schorlomite, schorlomite, and and goldmanite collectively lessless thanthan 3%.3%. OnOn a a local local scale, scale, these these garnets garnets are are continuously continuously zoned zoned with with Fe-rich Fe-rich cores cores and Al-richand Al-rich rims rims or exhibit or exhibit oscillatory oscillatory zoning, zoning, chemically chemically expressed expressed by variations by variations in Al-content. in Al-content. The garnets The garnetsfrom the from third the generation third generation form fine-grained form fine-grained aggregates aggregates in the quartz–calcitein the quartz–calcite matrix matrix and are and more are moregrossular-rich grossular-rich (grossular (gross componentular component 60–85%). 60–85%).

Figure 1. TransmittedTransmitted light light photomicrographs photomicrographs of of grossular–andradite grossular–andradite garnets garnets under crossed polarized light light ( (aa)) and and under under plane plane polarized polarized light light (b ();b ();c) (Ti-richc) Ti-rich garnet garnet in plane in plane polarized polarized light; light; (d) backscattered(d) backscattered electron electron images images of garnet of garnet skarn skarn show showinging a sharp a sharp contact contact between between Ti-rich Ti-rich andradite andradite and grossulareand grossulare of later of later generation. generation. AbbreviationsAbbreviations: Ap—apatite,: Ap—apatite, Grt—garnet, Grt—garnet, Prh—pehnite, Prh—pehnite, Cal—calcite, Cal—calcite, Qz—quartz, Grs—grossular, Ti-Grt—Ti-rich garnet, Adr—andradite, Prp—pyrope, Sch—schorlomite, Sps—spessartine, Alm—almandine.

The mineral composition of garnet skarn determined by XRPD is shown in Figure 2. The peaks of two type of garnets are well resolved in the patterns especially at d-spacing 2.99–2.97 Å, 2.67–2.65 Å. The grossular–andradite in this sample is modeled in the Rietveld analysis as a separate phase from grossular and both phases have unit cell dimensions that allow them to be distinguished in the diffraction patterns. Because of the relatively low abundance, Ti-rich andradite is not included in the refinements. The X-ray Rietveld refinements began with five major phases: quartz, calcite, grossular, grossular–andradite, and chlorite (Figure 3). No traces of the other minor phases could be detected in the diffraction pattern.

Minerals 2020, 10, 894 6 of 30

The mineral composition of garnet skarn determined by XRPD is shown in Figure2. The peaks of two type of garnets are well resolved in the patterns especially at d-spacing 2.99–2.97 Å, 2.67–2.65 Å. The grossular–andradite in this sample is modeled in the Rietveld analysis as a separate phase from grossular and both phases have unit cell dimensions that allow them to be distinguished in the diffraction patterns. Because of the relatively low abundance, Ti-rich andradite is not included in the refinements. The X-ray Rietveld refinements began with five major phases: quartz, calcite, grossular, grossular–andradite, and chlorite (Figure3). No traces of the other minor phases could be detected in Mineralsthe diff 2020raction, 10, x pattern. FOR PEER REVIEW 6 of 27

FigureFigure 2. X-rayX-ray powder powder diffraction diffraction patterns patterns of of a a garnet garnet skarn (d-spacings of the peaks are indicated).

The sequence of parameters, which were refined, is the following: scale factors for quartz, calcite, The sequence of parameters, which were refined, is the following: scale factors for quartz, calcite, grossular, grossular–andradite, chlorite (phases 1, 2, 3, 4 and 5); zero shift, background polynomial grossular, grossular–andradite, chlorite (phases 1, 2, 3, 4 and 5); zero shift, background polynomial parameters (six coefficients); unit cell parameters for all phases; half-width parameters for all phases parameters (six coefficients); unit cell parameters for all phases; half-width parameters for all phases (U, V, W); atomic site occupancies of Al and Fe in garnets (phases 3 and 4); atomic coordinates of (U, V, W); atomic site occupancies of Al and Fe in garnets (phases 3 and 4); atomic coordinates of phases 3 and 4; preferred orientation correction for phases 1 and 2. phases 3 and 4; preferred orientation correction for phases 1 and 2. Visualization of the fit is given in a difference plot on Figure3. The obtained quantities Visualization of the fit is given in a difference plot on Figure 3. The obtained quantities for the for the minerals present in the studied sample are (in wt%): quartz—30.41(1), calcite—34.40(3), minerals present in the studied sample are (in wt%): quartz—30.41(1), calcite—34.40(3), grossular grossular (Ca3Al1.8Fe0.2Si3O12)—21.41(3), grossular–andradite (Ca3Al0.9Fe1.1Si3O12)—12.78(4), chlorite (Ca3Al1.8Fe0.2Si3O12)—21.41(3), grossular–andradite (Ca3Al0.9Fe1.1Si3O12)—12.78(4), chlorite —~1(1). The —~1(1). The values of the standard agreement indices are Rp—10.4, Rwp—13.8, Rexp—8.61, GofF—1.6, values of the standard agreement indices are Rp—10.4, Rwp—13.8, Rexp—8.61, GofF—1.6, DW-Stat.— DW-Stat.—1.14. 1.14.

Figure 3. Rietveld refinement plot for garnet skarn. The rows of vertical lines give the positions of all

possible Bragg reflections for (from top to bottom) quartz, calcite, grossulare (Ca3Al1.8Fe0.2Si3O12),

grossular–andradite (Ca3Al0.9Fe1.1Si3O12), and chlorite.

Minerals 2020, 10, x FOR PEER REVIEW 6 of 27

Figure 2. X-ray powder diffraction patterns of a garnet skarn (d-spacings of the peaks are indicated).

The sequence of parameters, which were refined, is the following: scale factors for quartz, calcite, grossular, grossular–andradite, chlorite (phases 1, 2, 3, 4 and 5); zero shift, background polynomial parameters (six coefficients); unit cell parameters for all phases; half-width parameters for all phases (U, V, W); atomic site occupancies of Al and Fe in garnets (phases 3 and 4); atomic coordinates of phases 3 and 4; preferred orientation correction for phases 1 and 2. Visualization of the fit is given in a difference plot on Figure 3. The obtained quantities for the minerals present in the studied sample are (in wt%): quartz—30.41(1), calcite—34.40(3), grossular (Ca3Al1.8Fe0.2Si3O12)—21.41(3), grossular–andradite (Ca3Al0.9Fe1.1Si3O12)—12.78(4), chlorite —~1(1). The values of the standard agreement indices are Rp—10.4, Rwp—13.8, Rexp—8.61, GofF—1.6, DW-Stat.— Minerals 2020, 10, 894 7 of 30 1.14.

FigureFigure 3. Rietveld 3. Rietveld refinement refinement plot plot for for ga garnetrnet skarn. skarn. The The rows rows of of vertical vertical lines givegive thethe positions positions of of all all possible Bragg reflections for (from top to bottom) quartz, calcite, grossulare (Ca Al Fe Si O ), possible Bragg reflections for (from top to bottom) quartz, calcite, grossulare3 (Ca1.83Al0.21.8Fe3 0.212Si3O12), grossular–andradite (Ca3Al0.9Fe1.1Si3O12), and chlorite. grossular–andradite (Ca3Al0.9Fe1.1Si3O12), and chlorite. 4.2. Clinopyroxene–Garnet Skarn This is a fine- to coarse-grained rock containing garnets and clinopyroxene in quartz–calcite matrix with minor prehnite and chlorite. Accessory minerals include magnetite, apatite and titanite. The garnets in this sample, like those in garnet skarn, are represented by at least three generations: Ti-rich garnets, zoned coarse-grained grossular-andradites (Figure4a), and fine-grained grossular aggregates in quartz–calcite matrix. Grossular–andradites form poikiloblastic crystals that host relict minerals from the early high temperature contact metamorphic stage: melilite (Figure4d), wollastonite 2M (I generation) (Figure4c) and “fassaitic” clinopyroxene (I generation). Clinopyroxene − of the IInd generation commonly occurs as inclusions in garnet or as crystal aggregates in the quartz–calcite matrix, which exhibit strongly corroded margins. Optically, it shows strong dispersion of the optic axes, r > v, and displays anomalous blue and brown interference colors (Figure4b). The chemical compositions of the clinopyroxene from both generations are characterized by significant deficiency of SiO2, (Si 1.32–1.50 apfu) and high contents of esseneite (up to 46%) and Ca-Tschermak (up to 24%) components. Clinopyroxene of the Ist generation has lower content of esseneite (up to 20%). The mineral composition of clinopyroxene–garnet skarn determined by XRPD is shown in Figure5. The grossular–andradite in this sample is modeled in the Rietveld analysis as separate phases from grossular and clinopyroxene as esseneite. The XRPD Rietveld refinements incorporate only the six phases quartz, calcite, grossular, grossular–andradite, chlorite and clinopyroxene. No traces of the other minor phases could be detected in the diffraction pattern. According to optical and SEM studies Ti-rich andradite, melilite and wollastonite occur in quantities that are too small to be detected as discrete phases in the X-ray pattern. Clinopyroxenes from both generations could not be distinguished crystallographically. The sequence of the refined parameters is: scale factors for quartz, calcite, grossular, grossular-andradite, chlorite, clinopyroxene (phases 1, 2, 3, 4, 5, 6); zero shift; background polynomial parameters (six coefficients); unit cell parameters for phases 1, 2, 3, 4, 5, 6; half-width parameters for all phases (U, V, W); atomic site occupancies of Al and Fe in garnets (phases 3 and 4); atomic coordinates of phases 3 and 4; atomic site occupancies of Mg and Fe in clinopyroxene (phase 6) atomic coordinates of phase 6; preferred orientation correction for phases 1, 2 and 6. Minerals 2020, 10, x FOR PEER REVIEW 7 of 27

4.2. Clinopyroxene–Garnet Skarn This is a fine- to coarse-grained rock containing garnets and clinopyroxene in quartz–calcite matrix with minor prehnite and chlorite. Accessory minerals include magnetite, apatite and titanite. The garnets in this sample, like those in garnet skarn, are represented by at least three generations: Ti-rich garnets, zoned coarse-grained grossular-andradites (Figure 4a), and fine-grained grossular aggregates in quartz–calcite matrix. Grossular–andradites form poikiloblastic crystals that host relict minerals from the early high temperature contact metamorphic stage: melilite (Figure 4d), wollastonite−2M (I generation) (Figure 4c) and “fassaitic” clinopyroxene (I generation). Clinopyroxene of the IInd generation commonly occurs as inclusions in garnet or as crystal aggregates in the quartz–calcite matrix, which exhibit strongly corroded margins. Optically, it shows strong dispersion of the optic axes, r > v, and displays anomalous blue and brown interference colors (Figure 4b). The chemical compositions of the clinopyroxene from both generations are characterized by significant deficiency of SiO2, (Si 1.32–1.50 apfu) and high contents of esseneite (up to 46%) and Ca- Tschermak (up to 24%) components. Clinopyroxene of the Ist generation has lower content of esseneiteMinerals 2020 (up, 10 ,to 894 20%). 8 of 30

Minerals 2020, 10, x FOR PEER REVIEW 8 of 27 background polynomial parameters (six coefficients); unit cell parameters for phases 1, 2, 3, 4, 5, 6; half-width parameters for all phases (U, V, W); atomic site occupancies of Al and Fe in garnets (phases 3 andFigure 4); atomic 4. (a )coordinates Transmitted of light phases photomicrograph 3 and 4; atomic of site grossular–andradite occupancies of Mg garnet and showing Fe in clinopyroxene sectorial Figure 4. (a) Transmitted light photomicrograph of grossular–andradite garnet showing sectorial birefringence in the rim (crossed polarized light); (b) photomicrographs of “fassaitic” clinopyroxene with (phasebirefringence 6) atomic coordinatesin the rim (crossed of phase polarized 6; preferred light); (orientationb) photomicrographs correction of for“fassaitic” phases clinopyroxene 1, 2 and 6. anomalous blue and brown interference colors (transmitted crossed polarized light); (c) backscattered withThe Rietveldanomalous refinement blue and plot brown of theinterference fit is shown colors on Figure(transmitted 6. The crossed obtained polarized mineral light); quantities (c) in electron image of wollastonite (I generation) included in grossular–andradite garnet (polished section); clinopyroxene–garnetbackscattered electron skarn image ofare wollastonite (in wt%): (I gene quration)artz—17.65(2), included in calcite—41.31(2),grossular–andradite garnetgrossulare (d) backscattered electron image of melilite grains in garnet matrix (polished section). Abbreviations: (Ca3Al(polished1.8Fe0.2Si section);3O12)—18.55(1), (d) backscattered grossular–andradite electron image (Caof melilite3Al0.9Fe 1.1grainsSi3O 12in)—13.46(2), garnet matrix chlorite—~1(1), (polished Grt—garnet, Cpx—clinopyroxene, Prh—pehnite, Fas—“fassaitic” clinopyroxene, Woll—wollastonite, clinopyroxene—9.3(3).section). Abbreviations The: Grt—garnet, values of Cpx—clinopyroxene, the standard agreement Prh—pehnite, indices Fas—“fassaitic” are Rp—10.3, clinopyroxene, Rwp—13.9, R exp— Grs—grossular, Adr—andradite, Prp—pyrope, Mel—melilite. 8.49, Woll—wollastonite,GofF—1.1, DW-Stat.—1.22. Grs—grossular, Adr—andradite, Prp—pyrope, Mel—melilite.

The mineral composition of clinopyroxene–garnet skarn determined by XRPD is shown in Figure 5. The grossular–andradite in this sample is modeled in the Rietveld analysis as separate phases from grossular and clinopyroxene as esseneite. The XRPD Rietveld refinements incorporate only the six phases quartz, calcite, grossular, grossular–andradite, chlorite and clinopyroxene. No traces of the other minor phases could be detected in the diffraction pattern. According to optical and SEM studies Ti-rich andradite, melilite and wollastonite occur in quantities that are too small to be detected as discrete phases in the X-ray pattern. Clinopyroxenes from both generations could not be distinguished crystallographically. The sequence of the refined parameters is: scale factors for quartz, calcite, grossular, grossular-andradite, chlorite, clinopyroxene (phases 1, 2, 3, 4, 5, 6); zero shift;

Figure 5. X-rayX-ray powder powder diffraction diffraction patterns of a clinop clinopyroxene–garnetyroxene–garnet skarn (d-spacings of the peaks are indicated). The Rietveld refinement plot of the fit is shown on Figure6. The obtained mineral quantities in clinopyroxene–garnet skarn are (in wt%): quartz—17.65(2), calcite—41.31(2), grossulare (Ca3Al1.8Fe0.2Si3O12)—18.55(1), grossular–andradite (Ca3Al0.9Fe1.1Si3O12)—13.46(2), chlorite—~1(1),

Figure 6. Rietveld refinement plot for clinopyroxene–garnet skarn. The rows of vertical lines give the positions of all possible Bragg reflections for (from top to bottom) quartz, calcite, grossulare (Ca3Al1.8Fe0.2Si3O12), grossular–andradite (Ca3Al0.9Fe1.1Si3O12), chlorite and clinopyroxene.

Minerals 2020, 10, x FOR PEER REVIEW 8 of 27 background polynomial parameters (six coefficients); unit cell parameters for phases 1, 2, 3, 4, 5, 6; half-width parameters for all phases (U, V, W); atomic site occupancies of Al and Fe in garnets (phases 3 and 4); atomic coordinates of phases 3 and 4; atomic site occupancies of Mg and Fe in clinopyroxene (phase 6) atomic coordinates of phase 6; preferred orientation correction for phases 1, 2 and 6. The Rietveld refinement plot of the fit is shown on Figure 6. The obtained mineral quantities in clinopyroxene–garnet skarn are (in wt%): quartz—17.65(2), calcite—41.31(2), grossulare (Ca3Al1.8Fe0.2Si3O12)—18.55(1), grossular–andradite (Ca3Al0.9Fe1.1Si3O12)—13.46(2), chlorite—~1(1), clinopyroxene—9.3(3). The values of the standard agreement indices are Rp—10.3, Rwp—13.9, Rexp— 8.49, GofF—1.1, DW-Stat.—1.22.

Minerals 2020, 10, 894 9 of 30

Figure 5. X-ray powder diffraction patterns of a clinopyroxene–garnet skarn (d-spacings of the peaks clinopyroxene—9.3(3). The values of the standard agreement indices are R —10.3, R —13.9, are indicated). p wp Rexp—8.49, GofF—1.1, DW-Stat.—1.22.

Figure 6. Rietveld refinement plot for clinopyroxene–garnet skarn. The rows of vertical lines give Figurethe 6. positions Rietveld of refinement all possible plot Bragg for reflectionsclinopyroxene–garn for (from topet skarn. to bottom) The rows quartz, of calcite,vertical grossulare lines give the

positions(Ca3Al of1.8 Feall0.2 Sipossible3O12), grossular–andradite Bragg reflections (Ca for3Al 0.9(fromFe1.1 Sitop3O 12to), chloritebottom) and quartz, clinopyroxene. calcite, grossulare (Ca3Al1.8Fe0.2Si3O12), grossular–andradite (Ca3Al0.9Fe1.1Si3O12), chlorite and clinopyroxene. 4.3. Plagioclase-Clinopyroxene-Wollastonite-Garnet Skarn The rock is coarse- to fine-grained and contains garnet, wollastonite (II generation), plagioclase,

clinopyroxene, and calcite. Minor or secondary minerals present are Ti-rich andradite (Figure7a), quartz, prehnite, chlorite, and thaumasite. Accessory phases include titanite, apatite and magnetite. All of the constituent minerals are unevenly distributed within the zone. The rock is affected by intense retrograde processes represented by albitisation of former plagioclase, prehnitization of former wollastonite, and fracture-filling thaumasite (Figure7b,d). The garnets in this sample are grossular–andradites of intermediate composition (with andradite component from 42% to 50%) (Figure7c,d), but later almost pure andradite is also found (Figure7d). EPMA analysis and optical studies identified two types of clinopyroxene: “fassaitic” clinopyroxene (esseneite component—up to 50% and Ca-Tschermak—up to 19%) with anomalous blue and brown interference colors and clinopyroxene of the diopside–hedenbergite series (mean Wo51En41Fs8) (Figure7a). The mineral composition of Pl-Cpx-Wo-Grt skarn determined by XRPD is shown in Figure8. The Rietveld analysis starting set of the phases (grossular–andradite, clinopyroxene, plagioclase, wollastonite 2M, and calcite) was based on EPMA (Tables A1–A5), optical, single crystal, and XRPD − data. Clinopyroxenes from both types could not be distinguished because of the relatively low abundance of the “fassaitic” clinopyroxene and Rietveld analysis began with one pyroxene modeled as diopside–hedenbergite. Plagioclase is modeled as albite, garnet as grossular–andradite with intermediate composition, and wollastonite as wollastonite 2M. The sequence of refined − parameters is the following: scale factors for plagioclase, clinopyroxene, calcite, wollastonite 2M, − grossular–andradite (phases 1, 2, 3, 4, 5); zero shift, background polynomial parameters (22 coefficients); unit cell parameters for phases 1, 2, 3, 4, 5; half-width parameters for all phases (U, V, W); atomic site occupancies of Al and Fe in garnets (phase 5); atomic coordinates of phase 5; atomic site occupancies of Mg and Fe in clinopyroxene (phase 2); atomic coordinates of phase 2; preferred orientation correction for phases 1, 2, 3 and 4. Minerals 2020, 10, x FOR PEER REVIEW 9 of 27

4.3. Plagioclase-Clinopyroxene-Wollastonite-Garnet Skarn The rock is coarse- to fine-grained and contains garnet, wollastonite (II generation), plagioclase, clinopyroxene, and calcite. Minor or secondary minerals present are Ti-rich andradite (Figure 7a), quartz, prehnite, chlorite, and thaumasite. Accessory phases include titanite, apatite and magnetite. All of the constituent minerals are unevenly distributed within the zone. The rock is affected by intense retrograde processes represented by albitisation of former plagioclase, prehnitization of former wollastonite, and fracture-filling thaumasite (Figure 7b,d). The garnets in this sample are grossular–andradites of intermediate composition (with andradite component from 42% to 50%) (Figure 7c,d), but later almost pure andradite is also found (Figure 7d). EPMA analysis and optical studies identified two types of clinopyroxene: “fassaitic” clinopyroxene (esseneite component—up to 50% and Ca-Tschermak—up to 19%) with anomalous blue and brown interferenceMinerals 2020, 10 colors, 894 and clinopyroxene of the diopside–hedenbergite series (mean Wo51En1041 ofFs 308) (Figure 7a).

Figure 7. a Figure 7. ((a)) Transmitted Transmitted light photomicrograph showin showingg Ti-rich garnet, grossular–andradite and clinopiroxene of the diopside–hedenbergite series (plane polarized light); (b) photomicrographs clinopiroxene of the diopside–hedenbergite series (plane polarized light); (b) photomicrographs thaumasite (transmitted crossed polarized light); (c) backscattered electron image of wollastonite thaumasite (transmitted crossed polarized light); (c) backscattered electron image of wollastonite (II (II generation) and grossular–andradite garnet with intermediate composition (polished section); Mineralsgeneration) 2020, 10, x FORand PEERgrossular–andradite REVIEW garnet with intermediate composition (polished section); (d10) of 27 (d) backscattered electron image of “fassaitic” clinopyroxene included in grossular–andradite backscattered electron image of “fassaitic” clinopyroxene included in grossular–andradite garnet and garnet and later almost pure andradite (polished section). Abbreviations: Ti-Grt—Ti-rich occupancieslater almost of Al pure and andradite Fe in garnet (polisheds (phase section). 5); atomicAbbreviations: coordinates Ti-Grt—Ti-rich of phase garnet,5; atomic Grs—grossular, site occupancies garnet, Grs—grossular, And—andradite, Cpx—clinopyroxene, Fas—“fassaitic” clinopyroxene, of MgAnd—andradite, and Fe in clinopyroxene Cpx—clinopyrox (phaseene, Fas—“fassaitic”2); atomic coordinates clinopyroxene, of phase Woll—wollastonite, 2; preferred orientationPrp— Woll—wollastonite, Prp—pyrope, Thau—thaumasite. correctionpyrope, for Thau—thaumasite. phases 1, 2, 3 and 4.

The mineral composition of Pl-Cpx-Wo-Grt skarn determined by XRPD is shown in Figure 8. The Rietveld analysis starting set of the phases (grossular–andradite, clinopyroxene, plagioclase, wollastonite−2M, and calcite) was based on EPMA (Tables A1–A5), optical, single crystal, and XRPD data. Clinopyroxenes from both types could not be distinguished because of the relatively low abundance of the “fassaitic” clinopyroxene and Rietveld analysis began with one pyroxene modeled as diopside–hedenbergite. Plagioclase is modeled as albite, garnet as grossular–andradite with intermediate composition, and wollastonite as wollastonite−2M. The sequence of refined parameters is the following: scale factors for plagioclase, clinopyroxene, calcite, wollastonite−2M, grossular– andradite (phases 1, 2, 3, 4, 5); zero shift, background polynomial parameters (22 coefficients); unit cell parameters for phases 1, 2, 3, 4, 5; half-width parameters for all phases (U, V, W); atomic site

Figure 8. X-ray powder diffraction patterns of a Pl-Cpx-Wo-Grt skarn (d-spacings of the peaks are Figure 8. X-ray powder diffraction patterns of a Pl-Cpx-Wo-Grt skarn (d-spacings of the peaks are indicated). indicated). Figure9 shows the Rietveld refinement plot for the Pl-Cpx-Wo-Grt skarn. The obtained Figure 9 shows the Rietveld refinement plot for the Pl-Cpx-Wo-Grt skarn. The obtained mineral mineral quantities in this sample are (in wt%): plagioclase—46.69(2), clinopyroxene—22.30(1), quantities in this sample are (in wt%): plagioclase—46.69(2), clinopyroxene—22.30(1), wollastonite— 15.04(4), grossular–andradite—8.04(2), and calcite—7.93(1). The values of the standard agreement indices are Rp—18.63, Rwp—21.33, Rexp—17.29, GofF—1.23, DW-Stat.—1.24.

Figure 9. Rietveld refinement plots for the Pl-Cpx-Wo-Grt skarn. Above, the measured (blue line) and calculated pattern (red line) are presented, underneath the difference curve is given. Below, the reflection positions of the phases given in the upper right corner are displayed.

4.4. Plagioclase-clinopyroxene-wollastonite skarn This skarn rock is characterized by significant difference in the grain size of the constituent minerals. Minerals identified in thin section include plagioclase, clinopyroxene, wollastonite (Figure 10a,b) with minor or secondary Ti-rich andradite, calcite, quartz, prehnite, and chlorite. Titanite, apatite and magnetite occur as accessory phases. All of the minerals are unevenly distributed within the zone.

Minerals 2020, 10, x FOR PEER REVIEW 10 of 27

occupancies of Al and Fe in garnets (phase 5); atomic coordinates of phase 5; atomic site occupancies of Mg and Fe in clinopyroxene (phase 2); atomic coordinates of phase 2; preferred orientation correction for phases 1, 2, 3 and 4.

Figure 8. X-ray powder diffraction patterns of a Pl-Cpx-Wo-Grt skarn (d-spacings of the peaks are indicated). Minerals 2020, 10, 894 11 of 30 Figure 9 shows the Rietveld refinement plot for the Pl-Cpx-Wo-Grt skarn. The obtained mineral quantities in this sample are (in wt%): plagioclase—46.69(2), clinopyroxene—22.30(1), wollastonite— wollastonite—15.04(4), grossular–andradite—8.04(2), and calcite—7.93(1). The values of the standard 15.04(4), grossular–andradite—8.04(2), and calcite—7.93(1). The values of the standard agreement agreement indices are Rp—18.63, Rwp—21.33, Rexp—17.29, GofF—1.23, DW-Stat.—1.24. indices are Rp—18.63, Rwp—21.33, Rexp—17.29, GofF—1.23, DW-Stat.—1.24.

FigureFigure 9.9. Rietveld refinement refinement plots plots for for the the Pl-Cpx-Wo-Grt Pl-Cpx-Wo-Grt skarn. skarn. Above, Above, the measured the measured (blue (blue line) line)and Mineralsandcalculated 2020 calculated, 10, x patternFOR pattern PEER (red REVIEW (red line) line) are are presented, presented, undern underneatheath the the difference difference curv curvee is is given. given. Below, Below, the the11 of 27 reflectionreflection positionspositions ofof thethe phasesphases givengiven inin thethe upperupper rightright cornercorner areare displayed.displayed. The anorthite content in plagioclase in this sample (obtained from EPMA) shows large variations—from4.4.4.4. Plagioclase-Clinopyroxene-WollastonitePlagioclase-clinopyroxene-wollastonite 1.9% to 76.4% because skarn Skarnplagioclase is partially replaced by albite during the later retrograde processes (Figure 10c,d). The clinopyroxenes in this zone belong to the diopside– ThisThis skarn skarn rock rock is characterizedis characterized by significantby significant difference difference in the in grain the sizegrain of thesize constituent of the constituent minerals. hedenbergite series (Wo50En36–39Fs11–14). Wollastonite forms coarse poikiloblastic crystals that host Mineralsminerals. identified Minerals inidentified thin section in thin include section plagioclase, include plagioclase, clinopyroxene, clinopyroxene, wollastonite wollastonite (Figure 10a,b) (Figure with clinopyroxene and other rock-forming minerals (Figure 10a). Prehnite occurs in interstitial positions minor10a,b) orwith secondary minor or Ti-rich secondary andradite, Ti-rich calcite, andradite, quartz, calcite, prehnite, quartz, and prehnite, chlorite. and Titanite, chlorite. apatite Titanite, and or replaces earlier formed minerals. magnetiteapatite and occur magnetite as accessory occur as phases. accessory All ofphases. the minerals All of the are minerals unevenly are distributed unevenly distributed within the zone.within the zone.

Figure 10. (a,b) Transmitted light photomicrographs of Pl-Cpx-Wo skarn (plane polarized light); Figure 10. (a,b) Transmitted light photomicrographs of Pl-Cpx-Wo skarn (plane polarized light); (c,d) (c,d) backscattered electron images of Pl-Cpx-Wo skarn. Abbreviations: Woll—wollastonite, Cpx— backscattered electron images of Pl-Cpx-Wo skarn. Abbreviations: Woll—wollastonite, Cpx— clinopyroxene, Cal—calcite, Mag—magnetite, Ti-Grt—Ti-rich garnet, Pl—plagioclase, An—anorthite. clinopyroxene, Cal—calcite, Mag—magnetite, Ti-Grt—Ti-rich garnet, Pl—plagioclase, An—anorthite.

The mineral composition of Pl-Cpx-Wo skarn determined by XRPD is shown in Figure 11. The XRPD Rietveld refinement began with five phases: plagioclase, clinopyroxene, wollastonite−2M, calcite and prehnite. According to optical and EPMA (Tables A3, A4, A5, and A7) studies, the plagioclase is modeled as labradorite and clinopyroxene as diopside–hedenbergite. None of the other minor phases could be detected above background. The sequence of refined parameters is the following: scale factors for plagioclase, wollastonite−2M, clinopyroxene, calcite, prehnite (phases 1, 2, 3, 4, 5); zero shift; background polynomial parameters (22 coefficients); unit cell parameters for phases 1, 2, 3, 4, 5; half-width parameters for all phases (U, V, W); atomic site occupancies of Ca and Na in plagioclase (phase 1); atomic coordinates of phase 1; atomic site occupancies of Mg and Fe in clinopyroxene (phase 3); atomic coordinates of phase 3; preferred orientation correction for phases 1, 2, 3 4, and 5. Rietveld refinement plot of Pl-Cpx-Wo skarn is given in Figure 12. The obtained mineral quantities in this sample are (in wt%): plagioclase—32.15(3), wollastonite−2M—24.13(1), clinopyroxene—15.58(2), calcite—4.32(2), prehnite—23.81(4). The values of the standard agreement indices are Rp—13.66, Rwp—15.00, Rexp—13.76, GofF—1.09, DW-Stat.—1.97.

Minerals 2020, 10, 894 12 of 30

The anorthite content in plagioclase in this sample (obtained from EPMA) shows large variations—from 1.9% to 76.4% because plagioclase is partially replaced by albite during the later retrograde processes (Figure 10c,d). The clinopyroxenes in this zone belong to the diopside–hedenbergite series (Wo50En36–39Fs11–14). Wollastonite forms coarse poikiloblastic crystals that host clinopyroxene and other rock-forming minerals (Figure 10a). Prehnite occurs in interstitial positions or replaces earlier formed minerals. The mineral composition of Pl-Cpx-Wo skarn determined by XRPD is shown in Figure 11. The XRPD Rietveld refinement began with five phases: plagioclase, clinopyroxene, wollastonite 2M, − calcite and prehnite. According to optical and EPMA (Tables A3–A5 and A7) studies, the plagioclase is modeled as labradorite and clinopyroxene as diopside–hedenbergite. None of the other minor phases could be detected above background. The sequence of refined parameters is the following: scale factors for plagioclase, wollastonite 2M, clinopyroxene, calcite, prehnite (phases 1, 2, 3, 4, 5); zero − shift; background polynomial parameters (22 coefficients); unit cell parameters for phases 1, 2, 3, 4, 5; half-width parameters for all phases (U, V, W); atomic site occupancies of Ca and Na in plagioclase (phase 1); atomic coordinates of phase 1; atomic site occupancies of Mg and Fe in clinopyroxene (phase 3); atomic coordinates of phase 3; preferred orientation correction for phases 1, 2, 3 4, and 5. Rietveld refinement plot of Pl-Cpx-Wo skarn is given in Figure 12. The obtained mineral quantities in this sample are (in wt%): plagioclase—32.15(3), wollastonite 2M—24.13(1), clinopyroxene—15.58(2), − calcite—4.32(2), prehnite—23.81(4). The values of the standard agreement indices are Rp—13.66, MineralsRwp 2020—15.00,, 10, x FOR Rexp PEER—13.76, REVIEW GofF—1.09, DW-Stat.—1.97. 12 of 27

Figure 11. X-ray powder di raction patterns of Pl-Cpx-Wo skarn (d-spacings are indicated). Figure 11. X-ray powder diffractionff patterns of Pl-Cpx-Wo skarn (d-spacings are indicated).

Figure 12. Rietveld refinement plots for the Pl-Cpx-Wo skarn. Above, the measured (blue line) and calculated pattern (red line) are presented, underneath the difference curve is given. Below, the reflection positions of the phases given in the upper right corner are displayed.

4.5. Plagioclase-Clinopyroxene-Wollastonite-Epidote Skarn Pl-Cpx-Wo-Ep skarn is dominated by plagioclase, clinopyroxene, wollastonite, with subordinate ore minor epidote, calcite, quartz, chlorite, prehnite, and Ti-rich andradite, grossular-andradite (Figure 13a,d). Accessory minerals are titanite, apatite and magnetite. The rock is coarse- to fine- grained and characterized by unevenly distribution of the constituent minerals. According to EPMA and optical data, the mean content of the anorthite component in plagioclase is about 58%. Usually the primary plagioclase is partially replaced by albite. The clinopyroxenes in this zone belong to the diopside–hedenbergite series (Di36–80Hd21–63). The Fe3+/(Fe3+ + Al) ratio in the epidote composition ranges from 0.16 to 0.32. Locally, titanite forms porphyroblasts up to 1 mm long (Figure 13c). Prehnite occurs in interstitial positions or replaces the earlier formed plagioclase and wollastonite. The mineral composition of Pl-Cpx-Wo-Ep skarn determined by XRPD is presented in Figure 14. The XRPD Rietveld refinements incorporate eight phases: plagioclase, clinopyroxene, wollastonite−2M, calcite, epidote, prehnite, quartz, and chlorite. According to optical and EPMA (Tables A3–A7) studies the plagioclase is modeled as labradorite and clinopyroxene as diopside– hedenbergite. No traces of other minor phases could be detected in the diffraction pattern. The

Minerals 2020, 10, x FOR PEER REVIEW 12 of 27

Minerals 2020, 10, 894 13 of 30 Figure 11. X-ray powder diffraction patterns of Pl-Cpx-Wo skarn (d-spacings are indicated).

FigureFigure 12.12. RietveldRietveld refinementrefinement plotsplots forfor thethe Pl-Cpx-WoPl-Cpx-Wo skarn.skarn. Above, the measured (blue line) and calculatedcalculated patternpattern (red(red line)line) areare presented,presented, underneathunderneath thethe didifferencefference curvecurve isis given.given. Below, Below, the reflectionreflection positions positions of of thethe phasesphases givengiven inin thethe upperupper rightright cornercorner areare displayed.displayed.

4.5.4.5. Plagioclase-Clinopyroxene-Wollastonite-EpidotePlagioclase-Clinopyroxene-Wollastonite-Epidote SkarnSkarn Pl-Cpx-Wo-EpPl-Cpx-Wo-Ep skarn skarn isis dominateddominated byby plagioclase,plagioclase, clinopyroxene, wollastonite, with subordinate subordinate oreore minorminor epidote,epidote, calcite,calcite, quartz,quartz, chlorite,chlorite, prehnite,prehnite, andand Ti-richTi-rich andradite,andradite, grossular-andradite (Figure(Figure 1313a,d).a,d). Accessory Accessory minerals minerals are are titanite, titanite, apatite apatite and and magnetite. magnetite. The Therock rockis coarse- is coarse- to fine- to fine-grainedgrained and andcharacterized characterized by unevenly by unevenly distribution distribution of the of constituent the constituent minerals. minerals. AccordingAccording to to EPMA EPMA and and optical optical data, data, the mean the contentmean content of the anorthite of the anorthite component component in plagioclase in isplagioclase about 58%. is Usually about 58%. the primary Usually plagioclase the primary is partially plagioclase replaced is partially by albite. replaced The clinopyroxenes by albite. The in 3+ 3+ thisclinopyroxenes zone belong in to this the zone diopside–hedenbergite belong to the diopside–hedenbergite series (Di36–80Hd series21–63 (Di).36–80 TheHd Fe21–63/).(Fe The Fe+ 3+Al)/(Fe ratio3+ + Al) in theratio epidote in the compositionepidote composition ranges fromranges 0.16 from to 0.32.0.16 to Locally, 0.32. Locally, titanite titanite forms porphyroblastsforms porphyroblasts up to 1up mm to long1 mm (Figure long 13(Figurec). Prehnite 13c). Prehnite occurs in occurs interstitial in inters positionstitial orpositions replaces or the replaces earlier formedthe earlier plagioclase formed andplagioclase wollastonite. and wollastonite. TheThe mineralmineral composition composition of of Pl-Cpx-Wo-Ep Pl-Cpx-Wo-Ep skarn skarn determined determined by by XRPD XRPD is presentedis presented in Figurein Figure 14 . The14. XRPDThe RietveldXRPD Rietveld refinements refinements incorporate incorporat eight phases:e eight plagioclase, phases: clinopyroxene, plagioclase, wollastonite clinopyroxene,2M, − calcite,wollastonite epidote,−2M, prehnite, calcite, quartz, epidote, and prehnite, chlorite. quartz, According and to chlorite. optical andAccording EPMA (Tablesto optical A3 –andA7) studiesEPMA the(Tables plagioclase A3–A7) is studies modeled the as plagioclase labradorite is and modeled clinopyroxene as labradorite as diopside–hedenbergite. and clinopyroxene as No diopside– traces of otherhedenbergite. minor phases No traces could beof detectedother minor in the phases diffraction could pattern. be detected The sequence in the diffraction of refined parameterspattern. The is: scale factors for plagioclase, clinopyroxene, calcite, quartz, chlorite, wollastonite 2M, prehnite, epidote − (phases 1, 2, 3, 4, 5, 6, 7, 8); zero shift; background polynomial parameters (22 coefficients); unit cell parameters for all phases; half-width parameters for all phases (U, V, W); atomic site occupancies of Ca and Na in plagioclase (phase 1); atomic coordinates of phase 1; atomic site occupancies of Mg and Fe in clinopyroxene (phase 2); atomic coordinates of phase 2; atomic site occupancies of Al and Fe in epidote (phase 8); atomic coordinates of phase 8; preferred orientation correction for phases 1, 2, 3, 5, 6, 7 and 8. Rietveld refinement plot showing visually the quality of the fits for the Pl-Cpx-Wo-Ep skarn is given in Figure 15. The obtained results for mineral quantities in the sample are (in wt%): plagioclase—47.08(2), clinopyroxene—34.81(1), wollastonite 2M—5.01(3), calcite—3.84(2), − epidote—2.33(4), prehnite—2.78(2), quartz—1.67(1), and chlorite—2.49(2). The values of the standard indices of agreement are Rp—16.28, Rwp—18.36, Rexp—14.91, GofF—1.23, DW-Stat.—1.65. Minerals 2020, 10, x FOR PEER REVIEW 13 of 27 Minerals 2020, 10, x FOR PEER REVIEW 13 of 27 sequence of refined parameters is: scale factors for plagioclase, clinopyroxene, calcite, quartz, chlorite, wollastonite−2M, prehnite, epidote (phases 1, 2, 3, 4, 5, 6, 7, 8); zero shift; background polynomial parameters (22 coefficients); unit cell parameters for all phases; half-width parameters for all phases (U, V, W); atomic site occupancies of Ca and Na in plagioclase (phase 1); atomic coordinates of phase 1; atomic site occupancies of Mg and Fe in clinopyroxene (phase 2); atomic coordinates of phase 2; atomic site occupancies of Al and Fe in epidote (phase 8); atomic coordinates of phase 8; preferred Mineralsatomic 2020site, 10occupancies, 894 of Al and Fe in epidote (phase 8); atomic coordinates of phase 8; preferred14 of 30 orientation correction for phases 1, 2, 3, 5, 6, 7 and 8.

Figure 13. 13. TransmittedTransmitted light light photomicrographs photomicrographs of Pl-Cpx-Wo-Ep of Pl-Cpx-Wo-Ep skarn skarn under under plane plane polarized polarized light Figurea 13. Transmittedb light photomicrographs of Pl-Cpx-Wo-Epc skarn under plane polarized light light(a) and ( )(b and) under ( ) undercrossed crossed polarized polarized light; (c) light; photomicrograph ( ) photomicrograph of titanite of crystal titanite (plane crystal polarized (plane polarized(a) and (b) light); under (crossedd) backscattered polarized light; electron (c) imagesphotomicrograph of Pl-Cpx-Wo-Ep of titanite skarn crystal (polished (plane polarized section). light); (d) backscattered electron images of Pl-Cpx-Wo-Ep skarn (polished section). Abbreviations: Abbreviations:light); (d) backscattered Woll—wollastonite, electron images Cpx—clinopyroxene, of Pl-Cpx-Wo-Ep Prh—prehnite, skarn (polished Ttn—titanite; section). Abbreviations: Ti-Grt—Ti-rich Woll—wollastonite, Cpx—clinopyroxene, Prh—prehnite, Ttn—titanite; Ti-Grt—Ti-rich garnet, Pl— garnet,Woll—wollastonite, Pl—plagioclase, Cpx—clinopyroxene, Ep—epidote. Prh—prehnite, Ttn—titanite; Ti-Grt—Ti-rich garnet, Pl— plagioclase, Ep—epidote.

FigureFigure 14. 14.X-rayX-ray powder powder diffraction diffraction patterns patterns of Pl-C of Pl-Cpx-Wo-Eppx-Wo-Ep skarn skarn (d-spacings (d-spacings are are indicated). indicated).

Minerals 2020, 10, x FOR PEER REVIEW 14 of 27

Rietveld refinement plot showing visually the quality of the fits for the Pl-Cpx-Wo-Ep skarn is given in Figure 15. The obtained results for mineral quantities in the sample are (in wt%): plagioclase—47.08(2), clinopyroxene—34.81(1), wollastonite−2M—5.01(3), calcite—3.84(2), epidote— Minerals2.33(4),2020 prehnite—2.78(2),, 10, 894 quartz—1.67(1), and chlorite—2.49(2). The values of the standard indices15 of 30 of agreement are Rp—16.28, Rwp—18.36, Rexp—14.91, GofF—1.23, DW-Stat.—1.65.

FigureFigure 15.15. RietveldRietveld refinementrefinement plotsplots forfor thethe Pl-Cpx-Wo-EpPl-Cpx-Wo-Ep skarn.skarn. Above, the measured (blue line) andand calculated calculated patternpattern (red(red line)line) areare presented,presented, underneathunderneath the didifferfferenceence curve is given. Below, the reflectionreflection positions positions of of the the phases phases given given ininthe the upperupper rightright cornercorner areare displayed.displayed.

4.6.4.6. Plagioclase-ClinopyroxenePlagioclase-Clinopyroxene SkarnSkarn ThisThis skarnskarn isis presentpresent closeclose toto monzoniticmonzonitic rocksrocks inin contactcontact withwith thethe skarnskarn xenoliths.xenoliths. The rock is medium-grainedmedium-grained andand containscontains plagioclaseplagioclase andand clinopyroxeneclinopyroxene (Figure 1616a)a) with minor or secondary calcite,calcite, quartz, quartz, prehnite,prehnite, andand chlorite.chlorite. AccessoryAccessory mineralsminerals includeinclude titanite,titanite, apatiteapatite and magnetite. UsuallyUsually the the primary primary plagioclase plagioclase is partiallyis partially replaced replac byed albiteby albite or prehnite or prehni (Figurete (Figure 16b–d). 16b–d). The mean The plagioclasemean plagioclase composition composition measured measured by EPMA by EPMA is An 60is. An The60. clinopyroxeneThe clinopyroxene in this in this zone zone belongs belongs to the to diopside–hedenbergitethe diopside–hedenbergite series series (Di48–73 (Di48–73HdHd25–4925–49JhnJhn0–20–2)) and and formsforms zonedzoned crystalscrystals withwith Mg-richMg-rich cores andand Fe-richFe-rich rims rims (Figure (Figure 16c,d). 16c,d). Prehnite Prehnite occurs occurs in in interstitial interstitial positions positions or replaces or replaces the earlier the formed earlier formedMineralsplagioclase. 2020 plagioclase., 10 , x FOR PEER REVIEW 15 of 27 The mineral composition of Pl-Cpx skarn determined by XRPD is shown in Figure 17. The XRPD Rietveld refinements include five phases: plagioclase, clinopyroxene, calcite, quartz, and chlorite. Based on optical and EPMA (Tables A3 and A5) studies, the plagioclase is modeled as labradorite and clinopyroxene as diopside–hedenbergite. The minor phases are present only at the 0–2 vol.% level and could not be detected in the XRPD pattern. The obtained mean plagioclase composition is in agreement both with the mean of the optical determinations and with those measured by EPMA. The sequence of refined parameters is the following: scale factors for plagioclase, clinopyroxene, calcite, quartz, chlorite (phases 1, 2, 3, 4, 5); zero shift, background polynomial parameters (22 coefficients); unit cell parameters for phases 1, 2, 3, 4, 5; half-width parameters for all phases (U, V, W); atomic site occupancies of Ca and Na in plagioclase (phase 1); atomic coordinates of phase 1; atomic site occupancies of Mg and Fe in clinopyroxene (phase 2); atomic coordinates of phase 2; preferred orientation correction for phases 1, 2 and 3.

Figure 16. Transmitted light photomicrographs of Pl-CpxPl-Cpx skarn under plane polarized light (a) and

(b) underunder crossedcrossed polarizedpolarized light; (c,d) backscattered electron images of Pl-Cpx skarn sowing the zoned clinopyroxene crystals with Mg-rich cores andand Fe-rich rims (polished section). Abbreviations: Cpx—clinopyroxene, Pl—plagioclase,Pl—plagioclase, Prh—prehnite, An—anorthite.An—anorthite.

Figure 17. X-ray powder diffraction patterns of Pl-Cpx skarn (d-spacings are indicated).

Rietveld refinement plot for the Pl-Cpx skarn is shown in Figure 18. The obtained results for mineral quantities in the sample are (in wt%): plagioclase—41.16(3), clinopyroxene—40.69(5), calcite—14.15(2), quartz—1.29(2), and chlorite—2.72(1). The values of the standard indices of agreement are Rp—16.76, Rwp—16.37, Rexp—14.04, GofF—1.17, DW-Stat.—1.65.

Minerals 2020, 10, x FOR PEER REVIEW 15 of 27

Minerals 2020, 10, 894 16 of 30

The mineral composition of Pl-Cpx skarn determined by XRPD is shown in Figure 17. The XRPD Rietveld refinements include five phases: plagioclase, clinopyroxene, calcite, quartz, and chlorite. Based on optical and EPMA (Tables A3 and A5) studies, the plagioclase is modeled as labradorite and clinopyroxene as diopside–hedenbergite. The minor phases are present only at the 0–2 vol.% level and could not be detected in the XRPD pattern. The obtained mean plagioclase composition is in agreement both with the mean of the optical determinations and with those measured by EPMA. The sequence of refined parameters is the following: scale factors for plagioclase, clinopyroxene, calcite, quartz, chlorite (phases 1, 2, 3, 4, 5); zero shift, background polynomial parameters (22 coefficients); unit cell parameters forFigure phases 16. 1, Transmitted 2, 3, 4, 5; half-width light photomicrographs parameters for all of phases Pl-Cpx (U, skarn V, W); under atomic plane site polarized occupancies light of ( Caa) and Na(b) inunder plagioclase crossed (phase polarized 1); atomic light; ( coordinatesc,d) backscattered of phase electron 1; atomic images site occupanciesof Pl-Cpx skarn of Mg sowing and Fe the in clinopyroxenezoned clinopyroxene (phase 2);crystals atomic with coordinates Mg-rich cores of phase and 2;Fe-rich preferred rims orientation (polished section). correction Abbreviations: for phases 1, 2Cpx—clinopyroxene, and 3. Pl—plagioclase, Prh—prehnite, An—anorthite.

FigureFigure 17. 17.X-rayX-ray powder powder diffraction diffraction patterns patterns ofof Pl-CpxPl-Cpx skarn skarn (d-spacings (d-spacings are are indicated). indicated).

Rietveld refinement plot for the Pl-Cpx skarn is shown in Figure 18. The obtained results Rietveld refinement plot for the Pl-Cpx skarn is shown in Figure 18. The obtained results for for mineral quantities in the sample are (in wt%): plagioclase—41.16(3), clinopyroxene—40.69(5), mineralcalcite—14.15(2), quantities quartz—1.29(2),in the sample and are chlorite—2.72(1). (in wt%): plagioclase—41.16(3), The values of the standard clinopyroxene—40.69(5), indices of agreement calcite—14.15(2), quartz—1.29(2), and chlorite—2.72(1). The values of the standard indices of are Rp—16.76, Rwp—16.37, Rexp—14.04, GofF—1.17, DW-Stat.—1.65. agreement are Rp—16.76, Rwp—16.37, Rexp—14.04, GofF—1.17, DW-Stat.—1.65.

Minerals 2020, 10, 894 17 of 30 Minerals 2020, 10, x FOR PEER REVIEW 16 of 27

FigureFigure 18.18. RietveldRietveld refinementrefinement plotsplots forfor thethe Pl-CpxPl-Cpx skarn.skarn. Above, the measured (blue line) and calculatedcalculated patternpattern (red(red line)line) areare presented,presented, underneathunderneath thethe didifferencefference curvecurve isis given.given. Below, the reflectionreflection positions positions of of the the phases phases given given in in the the upper upperright rightcorner corner areare displayed.displayed.

5.5. DiscussionDiscussion TheThe quantitative quantitative analysis analysis of theof studiedthe studied skarn skar samplesn samples showed showed that the that Rietveld the methodRietveld combined method withcombined optical with and EPMAoptical studiesand EPMA is a suitablestudies approachis a suitable for quantificationapproach for ofquantification mineral concentrations. of mineral Thisconcentrations. combination This of methods combination was applied of methods in previous wa studiess applied to improvein previous the quantitative studies to determinationimprove the ofquantitative minerals [18 determination–20,24,25]. of minerals [18–20,24,25]. TheThe studiedstudied skarnskarn rocksrocks areare inhomogeneous,inhomogeneous, locallylocally veryvery fine-zoned,fine-zoned, containingcontaining mineral assemblagesassemblages fromfrom didifferentfferent stagesstages ofof thethe skarnskarn processes.processes. In addition, they consist of areas with significantsignificant didifferencesfferences in grain grain size—from size—from fine- fine- to to very very coarse-grained. coarse-grained. The Thepresence presence of minerals of minerals with withhighly highly variable variable mineralogical mineralogical compositions compositions and and chemically chemically zoned zoned crystals crystals further further complicate complicate the determinationdetermination of of phase phase quantities.quantities. InIn thisthis case,case, thethe estimationestimation of mineral content by routine methods suchsuch as as point-counting point-counting in in thin thin sections sections oror whole-rockwhole-rock analysesanalyses areare inappropriate.inappropriate. WhenWhen developingdeveloping aa RietveldRietveld XRPDXRPD quantificationquantification method,method, aa knowledgeknowledge of mineralogy and crystalcrystal structurestructure isis importantimportant factorfactor forfor thethe startingstarting setset ofof thethe phases.phases. TheThe refinedrefined crystal-structurecrystal-structure parametersparameters included included the the unit-cell unit-cell parameters parameters of each of phase each and phase element and substitutions element substitutions with pronounced with influencespronounced on intensitiesinfluences andon positionsintensities of and the reflections.positions of Atomic the reflections. positions andAtomic site occupanciespositions and can site be successfullyoccupancies varied can be forsuccessfu majorlly phases varied to for obtain major accurate phases scale to obtain factors. accurate For instance, scale factors. the Ca For2+ instance,and Na+ occupancythe Ca2+ and in plagioclaseNa+ occupancy structure; in plagioclase the Ca2+ structure;, Mg2+, Fe the2+, AlCa32++,Fe Mg3+2+occupancy, Fe2+, Al3+ Fe of3+ the occupancy octahedral of andthe tetrahedraloctahedral positionsand tetrahedral in the positions clinopyroxene in the structure;clinopyroxene the Ca structure;2+, Fe2+, the Fe3 +Ca, Al2+,3 Fe+,2+ and, Fe Ti3+,4 Al+ occupancy3+, and Ti4+ ofoccupancy the eight-coordinated of the eight-coordinated dodecahedral, 6-coordinateddodecahedral, octahedral, 6-coordinated and tetrahedraloctahedral, positions and tetrahedral in garnet structure;positions thein garnet Mg2+ andstructure; Fe2+ occupancy the Mg2+ and of theFe2+ octahedral occupancy positions of the octahedral in the chlorite positions structure; in the thechlorite Fe3+ andstructure; Al3+ occupancy the Fe3+ and in M3Al3+ octahedraloccupancy positionin M3 octahedral in epidote po structure.sition in epidote structure. TheThe resultsresults ofof somesome refinedrefined parametersparameters ofof thethe mineralsminerals fromfrom thethe studiedstudied skarnskarn samples are presentedpresented inin TablesTables2 –2–7.7. TheThe derived garnet compos compositionsitions of of grossular grossular and and grossular–andradite grossular–andradite of ofthe the garnet garnet skarn skarn by by Rietveld Rietveld XRPD XRPD method method are are in in good good agreement agreement with with the the data data of of the EPMA measurementsmeasurements (Tables (Tables2 2and and A1 A1).). TheThe refinedrefined unitunit cellcell parametersparameters ofof thethe “fassaitic”“fassaitic” typetype clinopyroxeneclinopyroxene from the clinopyroxene– garnetgarnet skarn skarn are are very very close close to to those those in in the the starting starting model model [48 ][48] and and the the compositions compositions of the of garnetsthe garnets and clinopyroxeneand clinopyroxene are in are accordance in accordance with thewith EPMA the EPMA data (Tablesdata (Tables3, A1 and3, A1 A2 and). A2). TheThe comparison comparison ofof thethe XRPDXRPD resultsresults withwith thethe EPMAEPMA analysesanalyses ofof thethe garnet,garnet, clinopyroxeneclinopyroxene and plagioclaseplagioclase compositions compositions from from Pl-Cpx-Wo-Grt Pl-Cpx-Wo-Grt skarn skarn (Tables (Tables4, A1, A34, andA1, A5A3) showsand A5) good shows agreement, good givenagreement, the presence given the of presence diopside–hedenbergite of diopside–hedenbe andrgite grossular–andradite and grossular–andradite solid solutions solid solutions and albite, and respectively.albite, respectively. The refined The unitrefined cell unit parameters cell parameters of the wollastonite of the wollastonite2M for− all2M samples for all samples are very are close very to − thoseclose reportedto those reported by Hesse by [49 Hesse] (Tables [49]4– (Tables6). 4–6). TableTable5 5presents presents refined refined parameters parameters of of the the minerals minerals from from the the Pl-Cpx-Wo Pl-Cpx-Wo skarn. skarn. TheThe averageaverage plagioclase composition of An40 derived by XRPD is slightly deficient in Ca relative to the mean value plagioclase composition of An40 derived by XRPD is slightly deficient in Ca relative to the mean obtained by EPMA (Table A5) but the pyroxene composition is well determined by XRPD, given the presence of cation isomorphic substitution in M1 site in the crystal structure (Tables 5 and A3). The

Minerals 2020, 10, 894 18 of 30 value obtained by EPMA (Table A5) but the pyroxene composition is well determined by XRPD, given the presence of cation isomorphic substitution in M1 site in the crystal structure (Tables5 and A3). The refined unit cell parameters of prehnite in the Pl-Cpx-Wo and Pl-Cpx-Wo-Ep skarns are close to those in the starting model [51].

Table 2. Some refined parameters in the quantitative analysis of the garnet skarn and chemical compositions of garnets determined by X-ray powder diffraction (XRPD) and electron probe microanalysis (EPMA).

Minerals Unit Cell Parameters (Å) Chemical Compositions starting model after refinement XRPD EPMA 2+ Ca3(Al1.8, (Ca2.96–2.98, Fe 0–0.04Mg0–0.1)3(Al1.66–1.81, Grossular a = 11.846(1) [45] a = 11.892(2) 3+ 3+ 2+ Fe 0.2)2Si3O12 Fe 0.17–0.26Ti0–0.01, Fe 0–0.01)2(Si,Al)3O12 Grossular– (Ca2.95–3.0, Mg0.01–0.08)3(Al0.77–0.95, a = 12.057 [44] a = 11.966(2) Ca3(Al0.9Fe1.1)2Si3O12 3+ 2+ andradite Fe 0.95–1.17Ti0–0.07, Fe 0–0.01)2(Si,Al)3O12

Table 3. Some refined parameters in the quantitative analysis of the clinopyroxene–garnet skarn and chemical compositions of the minerals determined by XRPD and EPMA.

Minerals Unit Cell Parameters (Å) Chemical Compositions starting model after refinement XRPD EPMA

Ca3(Al1.8, (Ca2.92–3.00, Mg0.05–0.09)3(Al1.58–1.80, Grossular a = 11.846(1) [45] a = 11.873(5) 3+ 3+ 2+ Fe 0.2)2Si3O12 Fe 0.12–0.30Fe 0–0.06)2(Si,Al)3O12 3+ Grossular– (Ca2.93–3.00, Mg0–0.07)3(Al0.78–0.94, Fe 1.00–1.10, a = 12.057 [44] a = 11.952(4) Ca3(Al0.9Fe1.1)2Si3O12 andradite Ti0–0.05)2(Si,Al)3O12 a = 9.79(1) [48] a = 9.77(1) 3+ 3+ VI b = 8.822(9) b = 8.83(1) Ca(Mg0.40Fe 0.40Al0.20) Ca(Mg0.26–0.47, Fe 0.31–0.44, Al 0.10–0.18, Clinopyroxene 2+ IV c = 5.37(1) c = 5.36(6) (Si1.4, Al0.6)2O6 Fe 0–0.14, Ti0.02–0.08)(Si1.32–1.48, Al 0.52–0.68)O6 β = 105.81(9) β = 105.78(1)

Table 4. Some refined parameters in the quantitative analysis of the Pl-Cpx-Wo-Grt skarn and chemical compositions of the minerals determined by XRPD and EPMA.

Minerals Unit Cell Parameters (Å) Chemical Compositions starting model after refinement XRPD EPMA 2+ Grossular– (Ca2.91–2.95, Mg0.06–0.09, Fe 0–0.02)3(Al0.70–1.07, a = 12.057 [44] a = 11,962(3) Ca3(Al0.9Fe1.1)2Si3O12 3+ 2+ andradite Fe 0.85–1.28, Ti0.01–0.06, Fe 0–0.02)2(Si,Al)3O12 a = 9.7456 [46] a = 9.789(3) Ca(Mg b = 8.9198 b = 8.928(3) 0.59–0.92 Clinopyroxene Ca(Mg Fe2+ )Si O Fe2+ Fe3+ Al )(Si , c = 5.2516 c = 5.260(2) 0.60 0.40 2 6 0.03–0.31 0–0.16 0–0.03 1.85–2.00 Al ) O β = 105.86 β = 105.77(1) 0–0.13 2 6 a = 8.137 [42] a = 8.140(2) b = 12.785 b = 12.780(4) c = 7.1583 c = 7.152(2) Na3.92–4.0Ca0–0.1K0–0.04 Plagioclase Na4Al4Si12O32 3+ α = 94.26 α = 94.176(2) Fe 0–0.03Al3.98–4.0Si11.95–11.97O32 β = 116.60 β = 116.562(2) γ = 87.71 γ = 87.90(1) a = 15.409 [49] a = 15.413(2) 2+ b = 7.322 b = 7.336(5) Ca1.92–1.96Mg0–0.03Fe 0.02–0.03 Wollastonite Ca2Si2O6 c = 7.063 c = 7.070(3) (Si1.96–1.99Al0.04–0.05)O6 β = 95.30 β = 95.24(5) Minerals 2020, 10, 894 19 of 30

Table 5. Some refined parameters in the quantitative analysis of the Pl-Cpx-Wo skarn and chemical compositions of the minerals determined by XRPD and EPMA.

Minerals Unit Cell Parameters (Å) Chemical Compositions starting model after refinement XRPD EPMA a = 9.7456 [46] a = 9.750(3) Ca Na (Mg Fe2+ b = 8.9198 b = 8.916(2) 0.99–1.0 0.01 0.65–0.72 0.21–0.25 Clinopyroxene Ca(Mg Fe2+ )Si O Fe3+ Al Cr Mn ) c = 5.2516 c = 5.258(1) 0.70 0.30 2 6 0–0.06 0–0.04 0–0.005 0.01–0.07 (Si Al ) O β = 105.86 β = 105.99(2) 1.96–1.99 0.01–0.04 2 6 a = 8.1736 [43] a = 8.150(2) b = 12.8736 b = 12.790(5) c = 7.1022 c = 7.140(1) Na0.99–3.92Ca0.07–2.50K0–0.5 Plagioclase Na2.4Ca1.6Al4Si12O32 3+ α = 93.462 α = 94.185(2) Mg0–0.18Fe 0–0.05Al4.03–7.5Si8.86–12O32 β = 116.054 β = 116.5432(3) γ = 90.475 γ = 88.81(1) a = 15.409 [49] a = 15.409(7) 2+ b = 7.322 b = 7.320(3) Ca1.97–1.99Mg0–0.02Fe 0.02Cr0–0.005 Wollastonite Ca2Si2O6 c = 7.063 c = 7.063(2) Mn0–0.05(Si1.98–1.99Al0–0.02)O6 β = 95.30 β = 95.36(3) a = 4.646 [51] a = 4.640(2) 3+ Prehnite b = 5.483 b = 5.482(2) Ca22 AlSi3O10(OH)2 Ca1.96–1.98Fe 0.01–0.18Ti0–0.02Al1.80–1.96Si3O10(OH)2 c = 18.486 c = 18.485(7)

The refined crystal chemical parameters of the minerals from the Pl-Cpx-Wo-Ep skarn are shown in Table6. The derived by XRPD mean plagioclase composition after refinement is in agreement both with the mean of the optical determinations and with those measured by EPMA (Table A5). The compositions of the clinopyroxene and the epidote are in good accordance with those determined by EPMA analyses (Tables A3 and A6). The results for Pl-Cpx skarn after refinements are presented in Table7. The variation of the Na /Ca content of the plagioclase during the XRPD refinement provided a composition of ~An50, in agreement with optical and EPMA data (Table A5). The pyroxene composition is in agreement with the EPMA results (Table A5).

Table 6. Some refined parameters in the quantitative analysis of the Pl-Cpx-Wo-Ep skarn and chemical compositions of the minerals determined by XRPD and EPMA.

Minerals Unit Cell Parameters (Å) Chemical Compositions starting model after refinement XRPD EPMA a = 9.7456 [46] a = 9.752(2) 2+ 3+ b = 8.9198 b = 8.919(2) 2+ Ca(Mg0.45–0.67Fe 0.23–0.44Fe 0.04–0.14 Clinopyroxene Ca(Mg0.60Fe 0.40)Si2O6 c = 5.2516 c = 5.262(7) Al0.01–0.06Ti0.01–0.03)(Si1.79–1.89Al0.11–0.21)2O6 β = 105.86 β = 106.10(1) a = 8.1736 [43] a = 8.167(3) b = 12.8736 b = 12.864(1) c = 7.1022 c = 7.122(1) Na0.13–3.24Ca0.50–3.77K0–0.11 Plagioclase Na1.8Ca2.1Al5Si12O32 3+ α = 93.462 α = 93.625(2) Fe 0–0.15Al4.31–7.41Si8.40–11.70O32 β = 116.054 β = 116.44(7) γ = 90.475 γ = 89.87(2) a = 15.409 [49] a = 15.377(1) 2+ b = 7.322 b = 7.299(4) Ca1.83–1.99Mg0–0.03Fe 0.02–0.05Cr0–0.005 Wollastonite Ca2Si2O6 c = 7.063 c = 7.049(5) Ti0–0.06(Si1.99–2.00Al0–0.01)O6 β = 95.30 β = 95.34(6) a = 4.646 [51] a = 4.640(2) 3+ Prehnite b = 5.483 b = 5.482(2) Ca22 AlSi3O10(OH)2 Ca1.93–2.00Fe 0.16–0.38Al1.60–1.78Si3O10(OH)2 c = 18.486 c = 18.485(7) a = 8.914 [50] a = 8.897(1) b = 5.640 b = 5.635(7) Ca (Al Fe3+)[Si O ] Ca (AlFe3+ )[Si O ] Epidote 2 2 2 7 21.98–2.39 0.49–0.96 2 7 c = 10.162 c = 10.152(1) [SiO4]O(OH) [SiO4]O(OH) β = 115.4 β = 115.378(4) Minerals 2020, 10, 894 20 of 30

Table 7. Some refined parameters in the quantitative analysis of the Pl-Cpx skarn and chemical compositions of the minerals determined by XRPD and EPMA.

Minerals Unit Cell Parameters (Å) Chemical Compositions starting model after refinement XRPD EPMA a = 9.7456 [46] a = 9.745(1) Ca Na (Mg Fe2+ b = 8.9198 b = 8.899(5) 0.95–0.97 0.02–0.04 0.42–0.60 0.21–033 Clinopyroxene Ca(Mg Fe2+ )Si O Fe3+ Al Ti V Mn Cr ) c = 5.2516 c = 5.252(3) 0.60 0.40 2 6 0.15–0.20 0–0.03 0.03–0.04 0–0.005 0.01 0–0.004 (Si Al Fe3+ ) O β = 105.86 β = 105.68(2) 1.74–1.81 0.19–0.23 0–0.02 2 6 a = 8.1736 [43] a = 8.174(2) b = 12.8736 b = 12.880(3) c = 7.1022 c = 7.112(2) Na0.47–3.26Ca0.52–3.59K0–0.11 Plagioclase Na1.9Ca2.0Al6Si12O32 3+ α = 93.462 α = 93.345(1) Fe 0–0.2Al4.57–7.32Si8.46–11.54O32 β = 116.054 β = 116.30(5) γ = 90.475 γ = 90.29(1)

The Rietveld refinement plots (Figures3,6,9, 12, 15 and 18) show the observed and calculated patterns for the studied samples. All of the refinements are acceptable, as can be judged by the standard indices of agreement and by the visual fits of the observed and calculated diffraction profiles, considering the complexity of the pattern and the large number of reflections. Each sample studied presents unique difficulties, as a result of its particular assemblages of minerals but the results show that the Rietveld XRPD method can be confidently applied to the wide range of rock types and phases under consideration here.

6. Conclusions In the present study, we have shown that accurate mineral quantification may be obtained by the Rietveld XRPD method from inhomogeneous fine-zoned skarn rocks. The method is equally applicable to fine-grained and coarse-grained rocks, and is useful in distinguishing between the components in solid solutions phases. The samples studied contain minerals with highly variable chemical compositions and involve up to eight major phases, causing significant overlap of peaks in the XRPD patterns. We demonstrate that the Rietveld XRPD method was able to refine these complex diffraction patterns. All of the refinements are acceptable, as can be judged by the standard indices of agreement and by the visual fit of the observed and calculated diffraction profiles. Summarizing the discussed quantitative approach, we may claim that the considered technique is a serious tool for accurate and time saving quantitative determination of mineral contents in complex geological materials that may give important mineralogical information leading to additional genetic conclusions.

Author Contributions: Collection of the samples and optical studies, Y.T.; EPMA and SEM analyses, Y.T. and M.T.; Rietveld refinement procedures, Y.T., O.P., and T.K.; writing—original draft preparation, Y.T. and O.P.; writing—review and editing, Y.T., O.P., T.K. and M.T.; visualization, Y.T., O.P., T.K., and M.T.; All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors of this paper are thankful to the reviewers for their constructive comments and suggestions, which helped us to improve considerably the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Minerals 2020, 10, 894 21 of 30

Appendix A

Table A1. Representative EPMA analyses and structural formulae of garnets from skarn rocks in the Zvezdel–Pcheloyad ore deposit (Fe2+ and Fe3+ according to the charge balance).

Skarn Type Grt Skarn Cpx-Grt Skarn Pl-Cpx-Wo-Grt No. of analyses 45-4-1 56 Gr-2-1 62 63 10 30 40 41 55-6-5 75 99 66 68 Oxides (wt%)

SiO2 37.72 39.20 36.47 39.22 36.51 39.80 38.80 39.64 36.16 37.49 36.41 37.16 36.57 37.20 TiO2 0.00 0.11 0.87 0.00 1.14 0.03 0.00 0.00 0.81 0.00 0.82 1.03 1.06 0.20 Al2O3 9.25 20.09 8.64 18.62 10.98 17.49 20.01 20.66 10.72 8.41 11.52 11.99 11.32 7.35 Fe2O3 16.91 3.84 19.43 4.61 15.75 6.18 2.95 2.11 16.35 18.34 14.88 14.47 15.20 21.61 MnO 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.08 0.09 0.00 0.00 0.00 0.00 0.00 MgO 0.12 0.00 0.17 0.85 0.70 0.70 0.41 0.77 0.61 0.00 0.65 0.76 0.75 0.51 CaO 36.23 36.11 34.23 36.42 34.46 35.49 36.87 37.17 33.82 36.63 34.28 34.18 34.29 33.82 Total 100.23 99.35 99.97 99.72 99.54 99.69 99.04 100.43 98.56 100.87 98.56 99.59 99.19 100.69 Structural formulae (a.p.f.u.) based on 12 oxygen atoms Si 3.008 3.000 2.948 2.991 2.917 3.057 2.965 2.975 2.924 2.986 2.928 2.952 2.926 2.998 AlIV 0.000 0.000 0.052 0.009 0.083 0.000 0.035 0.025 0.076 0.014 0.072 0.048 0.074 0.002 AlVI 0.869 1.811 0.770 1.663 0.951 1.582 1.765 1.801 0.945 0.775 1.019 1.074 0.992 0.696 Fe3+ 1.015 0.170 1.174 0.265 0.947 0.295 0.170 0.119 0.995 1.099 0.900 0.847 0.915 1.280 Ti 0.000 0.006 0.053 0.000 0.069 0.002 0.000 0.000 0.049 0.000 0.050 0.062 0.064 0.012 Fe2+ 0.000 0.012 0.007 0.000 0.000 0.063 0.000 0.000 0.000 0.000 0.000 0.017 0.000 0.012 Fe2+ 0.000 0.039 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.019 Mg 0.014 0.000 0.020 0.097 0.083 0.080 0.047 0.086 0.074 0.000 0.078 0.090 0.089 0.061 Mn 0.000 0.000 0.011 0.000 0.000 0.000 0.000 0.005 0.006 0.000 0.000 0.000 0.000 0.000 Ca 3.095 2.961 2.964 2.976 2.950 2.921 3.018 2.989 2.931 3.126 2.953 2.909 2.939 2.920 Adr 53.87 8.50 58.58 13.74 48.14 15.19 8.79 6.20 50.03 58.64 45.71 42.35 46.42 64.00 Grs 45.38 88.64 36.88 81.22 44.13 77.34 88.79 89.06 43.49 41.36 47.79 49.15 45.81 30.80 Prp 0.74 0.00 1.00 5.03 4.22 4.12 2.43 4.48 3.72 0.00 3.96 4.50 4.52 3.05 Sps 0.00 0.00 0.55 0.00 0.00 0.00 0.00 0.26 0.30 0.00 0.00 0.00 0.00 0.00 Schor + Morm 0.00 0.90 2.99 0.00 3.51 3.35 0.00 0.00 2.46 0.00 2.54 3.95 3.25 1.20 Alm 0.00 1.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.00 0.95 Notes: Adr, andradite; Grs, grossular; Prp, pyrope; Sps, spessartine; Uv, uvarovite; Schor+Morm, schorlomite+morimotoite; Gld, goldmanite; Alm, almandine. Minerals 2020, 10, 894 22 of 30

Table A2. Representative EPMA analyses and structural formulae of subsilicic aluminian ferrian diopside (“fassaite”) from skarn rocks in the Zvezdel–Pcheloyad ore deposit (Fe2+ and Fe3+ according to the charge balance).

Skarn Type Cpx-Grt Skarn Pl-Cpx-Wo-Grt No. of anal. P-9-4 P-4-1 Px-4-6 P-22 P-25 P-26 P-26a P-26b P-78 P-79 P-86 P-87 P-90 P-91 P-92 Oxides (wt%)

SiO2 34.00 33.54 34.79 39.10 39.07 38.86 38.92 39.00 35.95 36.63 38.91 34.16 36.67 37.37 36.10 TiO2 2.26 2.70 2.47 1.28 0.57 1.24 0.63 0.63 1.00 0.92 0.69 1.14 0.72 0.77 0.97 Al2O3 16.86 17.43 17.72 16.25 15.91 16.54 16.53 16.61 17.69 17.75 15.34 17.64 16.85 16.43 16.88 FeO 16.40 0.00 0.00 11.50 9.67 10.51 10.81 10.60 13.70 13.95 11.59 16.21 13.69 12.67 13.93 Fe2O3 0.00 17.67 17.32 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Cr2O3 0.00 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MnO 0.00 0.00 0.18 0.00 0.09 0.22 0.08 0.08 0.00 0.00 0.08 0.00 0.00 0.00 0.00 MgO 4.40 4.35 4.92 7.76 8.37 8.15 8.19 8.17 5.88 5.96 7.61 5.02 5.90 6.56 5.90 CaO 25.01 23.92 24.24 25.40 25.18 25.38 25.26 25.26 24.37 25.12 25.30 24.87 24.75 25.17 24.99 Total 98.93 99.61 101.7 101.3 98.86 100.9 100.4 100.4 98.59 100.3 99.52 99.04 98.58 98.97 98.77 Structural formulae (a.p.f.u.) based on 6 oxygen atoms Si 1.325 1.322 1.337 1.454 1.476 1.445 1.452 1.455 1.384 1.386 1.472 1.320 1.413 1.428 1.389 AlIV 0.675 0.678 0.663 0.546 0.524 0.555 0.548 0.545 0.616 0.614 0.528 0.680 0.587 0.572 0.611 AlVI 0.099 0.131 0.140 0.165 0.184 0.169 0.178 0.185 0.187 0.177 0.156 0.124 0.177 0.168 0.155 Ti 0.066 0.080 0.071 0.036 0.016 0.035 0.018 0.018 0.029 0.026 0.020 0.033 0.021 0.022 0.028 Fe3+ 0.441 0.383 0.374 0.308 0.305 0.315 0.333 0.322 0.368 0.382 0.330 0.487 0.366 0.357 0.398 Fe2+ 0.094 0.140 0.127 0.050 0.001 0.012 0.004 0.008 0.073 0.060 0.036 0.037 0.075 0.048 0.051 Cr 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Mg 0.256 0.256 0.282 0.430 0.472 0.452 0.455 0.454 0.338 0.336 0.429 0.289 0.339 0.374 0.339 Mn 0.000 0.000 0.006 0.000 0.003 0.007 0.003 0.003 0.000 0.000 0.003 0.000 0.000 0.000 0.000 Ca 1.044 1.010 0.998 1.012 1.019 1.011 1.009 1.010 1.006 1.019 1.026 1.030 1.022 1.031 1.031 Di+Hd 29.71 31.92 34.53 44.89 46.89 44.04 44.80 45.15 38.39 37.72 46.00 30.21 40.18 41.28 37.28 Ess 46.12 38.69 37.33 31.14 31.09 31.82 33.60 32.53 36.98 38.94 33.88 50.21 37.42 36.84 40.99 CaTs 10.36 13.23 13.97 16.68 18.76 17.07 17.96 18.69 18.79 18.04 16.02 12.78 18.10 17.34 15.96 S4(Mg) 13.81 16.16 14.17 7.28 3.26 7.07 3.63 3.64 5.83 5.30 4.11 6.80 4.29 4.54 5.77

Notes: Di, diopside; Hd, hedenbergite; Ess, esseneite; CaTs, Ca-Tschermak; S4 (Mg), component (CaMg0.5Ti4+0.5AlSiO6). Minerals 2020, 10, 894 23 of 30

Table A3. Representative EPMA analyses and structural formulae of clinopyroxenes of the diopside–hedenbergite series from skarn rocks in the Zvezdel–Pcheloyad ore deposit (Fe2+ and Fe3+ according to the charge balance).

Skarn Type Pl-Cpx-Wo-Ep Skarn Pl-Cpx-Wo-Grt Skarn Pl-Cpx-Wo Skarn Pl-Cpx Skarn No. of anal. P-15 P-17 P-18 P-19 P-20 P-21 13-11 P-104 P-94 11 12 12L 21 27 28 29 Oxides (wt%)

SiO2 49.30 50.05 50.44 49.04 47.63 49.00 56.21 49.29 49.21 52.09 51.25 51.22 45.15 44.54 45.85 47.61 TiO2 0.40 0.37 0.38 0.55 0.70 0.58 0.00 0.24 0.18 0.00 0.00 0.00 1.38 1.51 1.02 0.89 Al2O3 3.73 3.39 2.68 3.45 3.65 4.25 0.65 3.09 2.90 0.83 0.95 0.95 4.98 5.06 5.65 4.44 FeO 10.72 10.82 9.64 11.12 15.54 10.75 1.08 11.66 8.11 7.99 8.38 8.39 16.37 16.87 11.88 11.39 Cr2O3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.17 0.00 0.00 0.00 0.14 0.00 0.00 MnO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.23 0.16 0.38 0.38 0.38 0.36 0.32 0.22 0.18 V3O4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.13 0.17 0.00 0.11 MgO 10.11 10.78 11.91 10.24 7.69 10.00 16.73 10.23 12.47 12.77 12.31 12.3 7.51 7.26 9.67 10.54 CaO 25.32 25.41 25.13 24.77 23.87 24.80 24.06 24.15 25.28 24.68 24.54 24.54 22.89 22.71 23.49 23.9 Na2O 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.37 0.21 0.19 0.19 0.51 0.44 0.28 0.32 Total 99.58 100.82 100.18 99.17 99.08 99.38 98.73 98.89 98.68 99.12 98.00 98.9 99.28 99.02 98.06 99.38 Structural formulae (a.p.f.u.) based on 6 oxygen atoms Si 1.875 1.877 1.892 1.875 1.859 1.868 2.070 1.892 1.856 1.964 1.958 1.957 1.756 1.742 1.772 1.81 AlIV 0.125 0.123 0.108 0.125 0.141 0.132 0.000 0.108 0.129 0.036 0.042 0.043 0.228 0.233 0.228 0.19 Fe3+IV 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.015 0.000 0.000 0.000 0.016 0.025 0.000 0.000 AlVI 0.042 0.027 0.011 0.030 0.027 0.059 0.028 0.032 0.000 0.001 0.000 0.000 0.000 0.000 0.029 0.009 Ti 0.011 0.010 0.011 0.016 0.021 0.017 0.000 0.007 0.005 0.000 0.000 0.000 0.04 0.044 0.03 0.025 Fe3+ 0.059 0.075 0.075 0.063 0.073 0.039 0.000 0.061 0.161 0.045 0.056 0.055 0.201 0.197 0.161 0.153 Fe2+ 0.282 0.264 0.227 0.293 0.435 0.304 0.033 0.313 0.080 0.207 0.212 0.212 0.315 0.329 0.223 0.209 Cr 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.000 0.000 0.000 0.004 0.000 0.000 Mg 0.573 0.603 0.666 0.584 0.447 0.568 0.919 0.586 0.701 0.718 0.701 0.701 0.435 0.423 0.557 0.597 V 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.005 0.000 0.003 Mn 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.005 0.012 0.012 0.012 0.012 0.011 0.007 0.006 Ca 1.032 1.021 1.010 1.015 0.998 1.013 0.950 0.993 1.021 0.997 1.004 1.005 0.954 0.952 0.972 0.974 Na 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.027 0.015 0.014 0.014 0.038 0.033 0.021 0.024 Jd 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.03 0.01 0.00 0.00 1.18 0.49 Aeg 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.48 0.75 0.70 0.72 2.21 1.92 0.00 0.82 Ess 3.13 3.98 3.96 3.31 3.87 2.06 0.00 3.23 7.31 1.86 2.18 2.15 9.35 9.69 9.05 7.68 CTTs 0.61 0.55 0.56 0.84 1.09 0.88 0.00 0.37 0.28 0.00 0.00 0.00 2.32 2.56 1.67 1.41 CaTs 2.24 1.41 0.56 1.60 1.42 3.13 0.00 1.70 0.00 0.00 0.00 0.00 0.00 0.00 0.44 0.00 Wo 48.70 48.14 47.99 47.90 46.71 47.66 49.94 47.21 48.26 49.63 49.82 49.86 43.07 42.52 43.66 44.89 En 30.38 31.92 35.00 30.86 23.80 30.15 48.31 30.94 38.33 37.06 36.29 36.27 24.99 24.36 31.40 33.13 Fs 14.94 14.00 11.94 15.49 23.11 16.12 1.75 16.56 4.35 10.66 10.98 10.99 18.07 18.96 12.59 11.58

Notes: Jd, jadeite; Aeg, aegirine; Ess, esseneite; CTTs, component (CaTiAlAlO6); CaTs, Ca-Tschermak; Wo, wollastonite; En, enstatite; Fs, ferrosilite. Minerals 2020, 10, 894 24 of 30

Table A4. Representative EPMA analyses and structural formulae of wollastonite from skarn rocks in the Zvezdel–Pcheloyad ore deposit.

Pl-Cpx-Wo Skarn Type Pl-Cpx-Wo-Grt Skarn Pl-Cpx-Wo-Ep Skarn Skarn No. of anal. 103 67 70 71 72 73 77 81 18 19 1 10 31 6 W-2-1 W-2-2 Oxides (wt%)

SiO2 50.26 50.89 52.07 51.62 51.00 51.37 51.27 50.81 50.74 50.68 53.58 53.43 53.59 51.66 51.56 51.91 TiO2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.19 Al2O3 0.89 0.95 1.07 1.12 1.07 1.08 0.96 1.01 0.00 0.36 0.00 0.00 0.00 0.00 0.22 0.14 Cr2O3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.18 FeO 0.71 0.48 0.60 0.73 0.54 0.48 0.83 0.48 0.50 0.70 0.85 0.51 0.93 0.70 0.97 1.51 MnO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MgO 0.47 0.00 0.30 0.39 0.00 0.00 0.48 0.52 0.00 0.28 0.00 0.56 0.34 0.00 0.40 0.56 CaO 46.83 46.87 47.27 46.97 46.29 47.45 46.47 47.04 47.17 46.92 45.29 44.34 45.12 48.27 46.43 45.81 Total 99.16 99.19 101.31 100.83 98.90 100.38 100.01 99.86 98.72 98.94 99.72 98.84 99.98 100.63 99.58 100.30 Structural formulae (a.p.f.u.) based on 6 oxygen atoms Si 1.964 1.982 1.982 1.976 1.988 1.977 1.979 1.967 1.993 1.984 2.056 2.060 2.051 1.992 2.000 2.000 Al 0.041 0.044 0.048 0.050 0.049 0.049 0.044 0.046 0.000 0.017 0.000 0.000 0.000 0.000 0.010 0.006 Ti 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.006 Fe2+ 0.023 0.016 0.019 0.023 0.018 0.015 0.027 0.016 0.016 0.023 0.027 0.016 0.030 0.023 0.031 0.049 Cr 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.005 Mn 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Mg 0.027 0.000 0.017 0.022 0.000 0.000 0.028 0.030 0.000 0.016 0.000 0.032 0.019 0.000 0.023 0.032 Ca 1.960 1.956 1.928 1.926 1.933 1.957 1.922 1.951 1.985 1.968 1.862 1.832 1.850 1.994 1.930 1.891 Minerals 2020, 10, 894 25 of 30

Table A5. Representative EPMA analyses and structural formulae of plagioclase from skarn rocks in the Zvezdel–Pcheloyad ore deposit.

Skarn Pl-Cpx-Wo Skarn Pl-Cpx Skarn Pl-Cpx-Wo-Grt Skarn Pl-Cpx-Wo-Ep Skarn Type No. of anal. 01 14 20 18–13 23 24 25 31 33 Ab1 Ab1a 107 108 2 10 27 10 3 10 4 10 5 10 Oxides (wt%)

SiO2 67.65 67.26 41.67 61.58 44.44 54.64 64.17 51.88 63.85 67.41 67.42 67.80 68.47 44.98 64.53 51.87 66.29 51.70 Al2O3 19.36 19.19 29.82 22.24 32.68 26.17 21.22 27.77 21.65 19.04 19.05 19.40 19.43 33.69 21.03 30.27 20.71 30.19 Fe2O3 0.00 0.00 0.29 0.00 1.25 1.19 0.00 1.42 0.00 0.20 0.20 0.00 0.00 1.10 0.00 0.00 0.00 0.00 MgO 0.00 0.00 0.00 1.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 CaO 0.43 0.37 10.95 0.29 17.61 9.63 2.69 11.65 2.97 0.35 0.34 0.52 0.00 18.86 11.16 15.29 2.67 14.17 Na2O 11.43 10.74 2.39 11.18 1.27 5.60 9.35 4.43 9.57 11.46 11.48 11.47 12.08 0.35 1.70 2.14 9.47 2.82 K2O 0.08 0.00 0.00 1.32 0.00 0.49 0.10 0.26 0.08 0.19 0.17 0.00 0.00 0.00 0.50 0.00 0.00 0.00 Total 98.95 97.56 85.12 0.90 97.25 97.72 97.53 97.41 98.12 98.65 98.66 99.19 99.98 98.98 98.92 99.57 99.14 98.88 Structural formulae (a.p.f.u.) based on 32 oxygen atoms Si 11.952 12.007 8.863 11.087 8.456 10.109 11.544 9.685 11.447 11.963 11.962 11.948 11.972 8.402 11.461 9.446 11.704 9.470 Al 4.028 4.034 7.470 4.715 7.323 5.702 4.496 6.105 4.571 3.979 3.981 4.026 4.001 7.411 4.399 6.492 4.306 6.512 Fe3+ 0.000 0.000 0.046 0.000 0.179 0.166 0.000 0.199 0.000 0.027 0.027 0.000 0.000 0.154 0.000 0.000 0.000 0.000 Mg 0.000 0.000 0.000 0.178 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Ca 0.081 0.071 2.495 0.078 3.590 1.909 0.519 2.330 0.570 0.067 0.065 0.098 0.000 3.774 2.124 2.983 0.505 2.781 Na 3.916 3.717 0.986 2.157 0.469 2.009 3.262 1.604 3.327 3.943 3.950 3.919 4.096 0.127 0.585 0.756 3.242 1.002 K 0.018 0.000 0.000 0.461 0.000 0.116 0.023 0.062 0.018 0.043 0.038 0.000 0.000 0.000 0.113 0.000 0.000 0.000 Ab 97.50 98.10 28.30 16.30 11.60 49.80 85.80 40.10 85.00 97.30 97.50 97.60 100.0 3.30 20.70 20.20 86.50 26.50 An 2.00 1.90 71.70 76.40 88.40 47.30 13.60 58.30 14.60 1.70 1.60 2.40 0.00 96.70 75.30 79.80 13.50 73.50 Or 0.40 0.00 0.00 7.30 0.00 2.90 0.60 1.60 0.50 1.10 0.90 0.00 0.00 0.00 4.00 0.00 0.00 0.00 Notes: Ab, albite; An, anorthite; Or, orthoclase. Minerals 2020, 10, 894 26 of 30

Table A6. Representative EPMA analyses and structural formulae of epidote from skarn rocks in the Zvezdel–Pcheloyad ore deposit.

Skarn Type Pl-Cpx-Wo-Ep Skarn No. of anal. E25-7 E25-6 E27-6 Ep-6-8 E8-2-2 Ep-2-2 E19-1 E29-3 E19-2 E19-5 E29-6 E19-9 Oxides (wt%)

SiO2 38.63 38.59 36.73 37.76 37.36 37.59 37.82 37.24 37.42 36.93 37.22 37.15 Al2O3 25.64 25.62 20.41 22.35 20.53 21.30 23.45 21.28 22.12 23.71 22.96 24.08 Fe2O3 8.20 9.11 14.63 13.61 14.38 15.01 13.83 14.25 12.98 11.38 12.42 10.53 CaO 24.11 24.09 24.04 22.98 23.74 23.10 23.31 23.11 23.72 23.29 23.19 23.18 Total 96.58 97.41 95.81 96.70 96.01 97.00 98.41 95.88 96.24 95.31 95.79 94.94 Structural formulae (a.p.f.u.) based on 12.5 oxygen atoms Si 3.062 3.042 3.024 3.045 3.058 3.041 2.998 3.008 3.005 2.978 2.993 2.998 Al 2.394 2.378 1.979 2.122 1.979 2.029 2.191 2.026 2.094 2.253 2.176 2.290 Fe3+ 0.489 0.540 0.906 0.825 0.885 0.913 0.825 0.963 0.872 0.767 0.835 0.711 Ca 2.048 2.035 2.121 1.985 2.082 2.002 1.980 2.000 2.041 2.012 1.998 2.004 XFe 0.17 0.19 0.31 0.28 0.31 0.31 0.27 0.32 0.29 0.25 0.28 0.24 3+ 3+ XFe = Fe /(Fe + Al). Minerals 2020, 10, 894 27 of 30

Table A7. Representative EPMA analyses and structural formulae of prehnite from skarn rocks in the Zvezdel–Pcheloyad ore deposit.

Cpx-Grt Skarn Type Pl-Cpx-Wo-Grt Skarn Pl-Cpx-Wo+Ep Skarn Pl-Cpx-Wo Skarn Skarn No. of anal. 101 102 74 83 P26-6 P-7-2-9 69 11 3 4 9 Oxides (wt%)

SiO2 44.58 45.64 43.25 43.78 43.42 42.83 43.67 43.87 43.54 44.04 43.39 TiO2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.21 0.00 Al2O3 24.78 24.90 23.92 22.52 21.74 20.46 19.41 22.82 22.06 23.10 23.85 Fe2O3 0.95 0.00 0.62 2.08 2.99 4.28 7.15 1.89 3.38 1.86 0.23 MgO 0.00 0.00 0.00 0.33 0.00 0.00 0.00 0.29 0.00 0.00 0.00 CaO 26.77 27.25 27.32 27.28 27.72 27.68 25.77 25.94 26.53 26.57 26.53 Total 97.08 97.79 95.11 95.99 95.87 95.25 96.00 94.81 95.67 95.78 94.00 Structural formulae (a.p.f.u.) based on 11 oxygen atoms Si 3.013 3.052 2.997 3.020 3.016 3.014 3.053 3.046 3.020 3.031 3.028 Al 1.973 1.961 1.952 1.830 1.778 1.695 1.598 1.866 1.802 1.873 1.960 Fe3+ 0.048 0.000 0.032 0.108 0.156 0.226 0.376 0.099 0.176 0.096 0.012 Ti 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.017 0.022 0.000 Mg 0.000 0.000 0.000 0.034 0.000 0.000 0.000 0.030 0.000 0.000 0.000 Ca 1.939 1.952 2.028 2.016 2.063 2.087 1.930 1.929 1.972 1.960 1.983 Minerals 2020, 10, 894 28 of 30

References

1. Rietveld, H.M. Line profiles of neutron powder-diffraction peaks for structure refinement. Acta Crystallogr. 1967, 22, 151–152. [CrossRef] 2. Rietveld, H.M. A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 1969, 2, 65–71. [CrossRef] 3. Young, R.A.; Mackie, P.E.; Von Dreele, R.B. Application of the pattern-fitting structure-refinement method to X-ray powder diffractometer patterns. J. Appl. Cryst. 1977, 10, 262–269. [CrossRef] 4. Hill, R.J. X-ray powder diffraction profile refinement of synthetic hercynite. Am. Mineral. 1984, 69, 937–942. 5. Cox, D.E.; Hastings, J.B.; Thomlinson, W.; Prewitt, C.T. Application of synchrotron radiation to high resolution powder diffraction and Rietveld refinement. Nucl. Instrum. Methods Phys. Res. 1983, 208, 573–578. [CrossRef] 6. Bish, D.L. Rietveld refinement of the kaolinite structure at 1.5 K. Clays Clay Miner. 1993, 41, 738–744. [CrossRef] 7. Albinati, A.; Willis, B.T.M. The Rietveld method in X-ray and neutron powder diffraction. J. Appl. Crystallogr. 1982, 15, 361–374. [CrossRef] 8. Hill, R.J. Calculated X-ray powder diffraction data for phases encountered in lead/acid battery plates. J. Power Sources 1983, 9, 55–71. [CrossRef] 9. Hill, R.J.; Madsen, I.C. Data collection strategies for constant wavelength Rietveld analysis. Powder Diffr. 1987, 2, 146–162. [CrossRef] 10. Hill, R.J.; Howard, C.J. Quantitative phase analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Cryst. 1987, 20, 467–474. [CrossRef] 11. Bish, D.L.; Howard, S.A. Quantitative phase analysis using the Rietveld method. J. Appl. Crystallogr. 1988, 21, 86–91. [CrossRef] 12. Post, J.E.; Bish, D.L. Rietveld Refinement of Crystal Structures Using Powder X-Ray Diffraction Data. In Modern Powder Diffraction; Reviews in Mineralogy; Bish, D.L., Post, J.E., Eds.; Mineralogical Society of America: Washington, DC, USA, 1989; Volume 20, pp. 277–308. 13. Snyder, R.L.; Bish, D.L. Quantitative Analysis. In Modern Powder Diffraction; Reviews in Mineralogy; Bish, D.L., Post, J.E., Eds.; Mineralogical Society of America: Washington, DC, USA, 1989; Volume 20, pp. 277–308. 14. Hill, R.J. Expanded use of the Rietveld method in studies of phase abundance in multiphase mixtures. Powder Diffr. 1991, 6, 74–77. [CrossRef] 15. Young, R.A. Introduction to the Rietveld Method. In The Rietveld Method; International Union of Crystallography, Monographs in Crystallography; Young, R.A., Ed.; Oxford University Press: New York NY, USA, 1993; pp. 1–38. 16. Bish, D.L.; Post, J.E. Quantitative mineralogical analysis using the Rietveld full-pattem fitting method. Am. Mineral. 1993, 78, 932–940. 17. McCusker, L.B.; Von Dreele, R.B.; Cox, D.E.; Louër, D.; Scardi, P. Rietveld refinement guidelines. J. Appl. Cryst. 1999, 32, 36–50. [CrossRef] 18. Hill, R.J.; Tsambourakis, G.; Madsen, I.C. Improved petrological modal analyses from X-ray powder diffraction data by use of the Rietveld method I. Selected igneous, volcanic, and metamorphic rocks. J. Pet. 1993, 34, 867–900. [CrossRef] 19. Mumme, W.G.; Tsambourakis, G.; Madsen, I.C.; Hill, J.R. Improved petrological modal analyses from X-ray powder diffraction data by use of the Rietveld method. Part II. Selected sedimentary rocks. J. Sediment. Res. 1996, 66, 132–138. 20. Mumme, W.G.; Tsambourakis, G.; Cranswick, L.M.D. Improved petrological modal analyses from X-ray and neutron powder diffraction data by use of the Rietveld method. Part 3. Selected massive sulphide ores. J. Petrl. 1996, 170, 231–255. 21. Taylor, J.C.; Matulis, C.E. A new method for Rietveld clay analysis. Part, I. Use of a universal measured standard profile for Rietveld quantification of montmorillonites. Powder Diffr. 1994, 9, 119–123. [CrossRef] 22. Raudsepp, M.; Pani, E.; Dipple, G.M. Measuring mineral abundance in skarn. I. The Rietveld method using X-ray powder-diffraction data. Can. Miner. 1999, 37, 1–15. 23. Monecke, T.; Köhler, S.; Kleeberg, R.; Herzig, P.; Gemmell, J.B. Quantitative phase-analysis by the Rietveld method using X-ray powder-diffraction data: Application to the study of alteration halos associated with volcanic-rock-hosted massive sulfide deposits. Can. Mineral. 2001, 39, 1617–1633. [CrossRef] Minerals 2020, 10, 894 29 of 30

24. Webster, J.R.; Kight, R.P.; Winburn, R.S.; Cool, C.A. Heavy mineral analysis of sandstones by Rietveld analysis. Adv. X-ray Anal. 2003, 46, 198–203. 25. Gonzalez, R.M.; Edwards, T.E.; Lorbiecke, T.D.; Winburn, R.S.; Webster, J.R. Analysis of geologic materials using Rietveld quantitative X-ray diffraction. Adv. X-Ray Anal. 2003, 46, 204–209. 26. Oerter, E.J.; Brimhall, G.H., Jr.; Redmond, J.; Walker, B. A method for quantitative pyrite abundance in mine rock piles by powder X-ray diffraction and Rietveld refinement. Appl. Geochem. 2007, 22, 2907–2925. [CrossRef] 27. Ufer, K.; Stanjek, H.; Roth, G.; Dohrmann, R.; Kleeberg, R.; Kaufhold, S. Quantitative phase analysis of bentonites by the Rietveld method. Clays Clay Miner. 2008, 56, 272–282. [CrossRef] 28. Snellings, R.; Machiels, L.; Mertens, G.; Elsen, J. Rietveld refinement strategy for quantitative phase analysis of partially amorphous zeolitized tuffaceous rocks. Geol. Belg. 2010, 13, 183–196. 29. Hestnes, K.H.; Sørensen, B.E. Evaluation of quantitative X-ray diffraction for possible use in the quality control of granitic pegmatite in mineral production. Min. Eng. 2012, 39, 239–247. [CrossRef] 30. Gentili, S.; Comodi, P.; Bonadiman, C.; Coltorti, M. Mass balance vs Rietveld refinement to determine the modal composition of ultramafic rocks: The case study of mantle peridotites from Northern Victoria Land (Antarctica). Tectonophysics 2015, 650, 144–145. [CrossRef] 31. Santini, T.C. Application of the Rietveld refinement method for quantification of mineral concentrations in bauxite residues (alumina refining tailings). Int. J. Miner. Process. 2015, 139, 1–10. [CrossRef] 32. Santos, H.N.; Neumann, R.; Ávila, C.A. Mineral quantification with simultaneous refinement of Ca-Mg carbonates non-stoichiometry by X-ray diffraction, Rietveld method. Minerals 2017, 7, 164. [CrossRef] 33. Dietel, J.; Ufer, K.; Kaufhold, S.; Dohrmann, R. Crystal structure model development for soil clay minerals—II. Quantification and characterization of hydroxy-interlayered smectite (HIS) using the Rietveld refinement technique. Geoderma 2019, 347, 1–12. [CrossRef] 34. Nedialkov, R.; Mavroudchiev, B. Geochemical and mineralogical peculiarities of the Zvezdel pluton (East Rhodopes, Bulgaria). In Proceedings of the XV Congress of the Carpatho-Balcan Geological Association, Geol. Soc., Athens, Greece, 17–20 September 1995; pp. 561–565. 35. Tzvetanova, Y. Crystal-Chemical and Structural Characteristics of Minerals from Skarns in Zvezdel Pluton. Ph.D. Thesis, Institute of Mineralogy and Crystallography, Bulgarian Academy of Sciences, Sofia, Bulgaria, 2015. 36. Tzvetanova, Y.; Kadyiski, M.; Petrov, O. Parawollastonite (wollastonite-2M polytype) from the skarns in Zvezdel pluton, Eastern Rhodopes—A single crystal study. Bulg. Chem. Commun. 2012, 44, 131–136. 37. Powder Diffraction File (PDF-2 Data Base 2001); International Centre for Diffraction Data (ICDD): Newtown Square, PA, USA, 2001. 38. Rodriguez-Carvajal, J.; Roisnel, T. FullProf.98 and WinPLOTR New Windows 95/NT Applications for Diffraction. Newsletter No 20. Commission for Powder Diffraction; International Union for Crystallography: Chester, UK, 1998. 39. Roisnel, T.; Rodríguez-Carvajal, J. WinPLOTR: A Windows tool for powder diffraction patterns analysis. Mater. Sci. Forum 2001, 378, 118–123. [CrossRef] 40. Rodriguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Phys. B Condens. Matter. 1993, 192, 55–69. [CrossRef] 41. Topas V 4.2: General Profile and Structure Analysis Software for Powder Diffraction; Bruker AXS: Karlsruhe, Germany, 2009. 42. Armbruster, T.; Bürgi, H.B.; Kunz, M.; Gnos, E.; Brönnimann, S.; Lienert, C. Variation of displacement parameters in structure refinements of low albite. Am. Mineral. 1990, 75, 135–140. 43. Wenk, H.R.; Joswig, W.; Tagai, T.; Korekawa, M.; Smith, B.K. The average structure of an 62–66 labradorite. Am. Mineral. 1980, 65, 81–95. 44. Lager, G.A.; Armbruster, T.; Rotella, F.J.; Rossman, G.R. OH substitution in garnets: X-ray and neutron diffraction, infrared and geometric-modeling studies. Am. Mineral. 1989, 74, 840–851. 45. Hazen, R.M.; Finger, L.W. Crystal structures and compressibilities of pyrope and grossular to 60 kbar. Am. Mineral. 1978, 63, 297–303. 46. Levien, L.; Prewitt, C.T. High-pressure structural study of diopside. Am. Mineral. 1981, 66, 315–323. 47. Cameron, M.; Sueno, S.; Prewitt, C.T.; Papike, J.J. High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite, spodumene, and ureyite. Am. Mineral. 1973, 58, 594–618. Minerals 2020, 10, 894 30 of 30

48. Cosca, M.A.; Peacor, D.R. Chemistry and structure of esseneite (CaFe 3+ AlSiO 6), a new pyroxene produced by pyrometamorphism. Am. Miner. 1987, 72, 148–156. 49. Hesse, K.F. Refinement of the crystal structure of wollastonite-2M (parawollastonite). Z. Kristallogr. 1984, 168, 93–98. [CrossRef] 50. Dollase, W.A. Refinement of the crystal structures of epidote, allanite and hancockite. Am. Mineral. 1971, 56, 447–464. 3 51. Papike, J.J.; Zoltai, T. Ordering of tetrahedral aluminium in prehnite, Ca2(Al, Fe+ ) [Si3AlO10](OH)2. Am. Mineral. 1967, 52, 974–984. 52. Effenberger, H.; Mereiter, K.; Zemann, J. Crystal structure refinements of magnesite, calcite, rhodochrosite, siderite, smithsonite, and dolomite, with discussions of some aspects of the stereochemistry of calcite-type carbonates. Z. Kristallogr. 1981, 156, 233–243. 53. Levien, L.; Prewitt, C.T.; Weidner, D.J. Structure and elastic properties of quartz at pressure. Am. Mineral. 1980, 65, 920–930. 54. Zanazzi, P.F.; Comodi, P.; Nazzareni, S.; Andreozzi, G.B. Thermal behaviour of chlorite: An in situ single-crystal and powder diffraction study. Eur. J. Mineral. 2009, 21, 581–589. [CrossRef] 55. Hill, R.J.; Madsen, I.C. Rietveld analysis using para-focusing and Debye-Scherrer geometry data collected with a Bragg-Brentano diffractometer. Z. Kristallogr. 1991, 196, 73–92. [CrossRef] 56. Young, R.A.; Prince, E.; Sparks, R.A. Suggested guidelines for the publication of Rietveld analyses and pattern decomposition studies. J. Appl. Cryst. 1982, 15, 357–359. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).